Sources

1) Source: The Henry Project . External Link
https://fasg.org/projects/henryproject/data/ingra000.htm. Reference: Ingram (Questionable reliability of evidence)
2) Source: Vita Hludovici Imperatoris "Supradictus vero Hludowicus postquam ad aetatem pervenit, desponsavit sibi filiam nobilissimi ducis Ingorammi, qui erat filius fratris Hruotgangi, sancti pontificis. Supradicta vero virgo Irmingarda vocabatur, quam cum consilio et consensu patris reginam constituit, atque ex ea tres filios habuit adhuc vivente patre, quorum unus vocabatur Hlutharius, alter Pippinus, tertius aequivocus eius Hludowicus.". Reference: 4 (Data from direct source)
3) Source: The Henry Project . External Link
https://fasg.org/projects/henryproject/data/ermen006.htm. Reference: Ermengarde (Questionable reliability of evidence)
4) Source: Carolingian Chronicles: Royal Frankish Annals and Nithard's Histories "823... in the meantime Queen Irmengardis, their mother, died, and a short time later Emperor Louis married Judith, who gave birth to Charles.". Reference: Nithard's Histories (Data from secondary evidence)
5) Source: Genealogia comitum Bulonensium A short genealogy connecting the early Merovingians to the later counts of Boulogne, written circa the 11th century. The earliest generations are almost certainly fictional. Considered a reliable secondary source for generations from Arnulf of Metz onwards. Considered a "primary" source for events from the year 1000 onwards.. External Link
https://www.dmgh.de/mgh_ss_9/index.htm#page/300/ (Data from secondary evidence)
6) Source: Carolingian Chronicles: Royal Frankish Annals and Nithard's Histories "818... Queen Irmengardis, his wife, whom he had left behind sick, died of her ailments two days after his return on October 3.". Reference: RFA (Data from secondary evidence)
7) Source: Vita Hludovici Imperatoris "Inde regrediens invenit Irmingardam reginam febricitantem, quae non post multos dies obiit in pace.". Reference: 25 (Data from secondary evidence)