Base field 6.6.1202933.1
Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} - 2x^{3} + 6x^{2} + x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[19, 19, w^{5} - w^{4} - 5w^{3} + 2w^{2} + 4w]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 3x^{6} - 20x^{5} + 48x^{4} + 108x^{3} - 144x^{2} - 144x + 80\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^{4} + w^{3} + 4w^{2} - 2w - 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 4w - 3]$ | $-\frac{3}{124}e^{6} + \frac{1}{124}e^{5} + \frac{73}{124}e^{4} - \frac{1}{124}e^{3} - \frac{215}{62}e^{2} - \frac{34}{31}e + \frac{69}{31}$ |
| 19 | $[19, 19, w^{5} - w^{4} - 5w^{3} + 2w^{2} + 4w]$ | $-1$ |
| 23 | $[23, 23, -w^{2} + w + 2]$ | $-\frac{21}{248}e^{6} + \frac{69}{248}e^{5} + \frac{89}{62}e^{4} - \frac{515}{124}e^{3} - \frac{303}{62}e^{2} + \frac{284}{31}e + \frac{102}{31}$ |
| 25 | $[25, 5, w^{5} + w^{4} - 6w^{3} - 7w^{2} + 4w + 2]$ | $-\frac{1}{124}e^{6} + \frac{21}{124}e^{5} - \frac{17}{124}e^{4} - \frac{331}{124}e^{3} + \frac{83}{31}e^{2} + \frac{216}{31}e - \frac{8}{31}$ |
| 41 | $[41, 41, 2w^{5} - w^{4} - 10w^{3} + 6w - 1]$ | $-\frac{5}{62}e^{6} + \frac{6}{31}e^{5} + \frac{35}{31}e^{4} - \frac{167}{62}e^{3} - \frac{38}{31}e^{2} + \frac{207}{31}e - \frac{18}{31}$ |
| 47 | $[47, 47, w^{3} - w^{2} - 4w]$ | $-e^{2} + e + 8$ |
| 53 | $[53, 53, w^{5} - 5w^{3} - 3w^{2} + w + 3]$ | $\phantom{-}\frac{2}{31}e^{6} - \frac{13}{124}e^{5} - \frac{28}{31}e^{4} + \frac{137}{124}e^{3} + \frac{49}{31}e^{2} - \frac{54}{31}e - \frac{91}{31}$ |
| 59 | $[59, 59, 2w^{5} - 11w^{3} - 4w^{2} + 8w]$ | $\phantom{-}\frac{3}{62}e^{6} - \frac{33}{124}e^{5} - \frac{115}{124}e^{4} + \frac{140}{31}e^{3} + \frac{153}{31}e^{2} - \frac{459}{31}e - \frac{76}{31}$ |
| 61 | $[61, 61, w^{2} - 2w - 2]$ | $-\frac{7}{124}e^{6} + \frac{23}{124}e^{5} + \frac{129}{124}e^{4} - \frac{333}{124}e^{3} - \frac{132}{31}e^{2} + \frac{117}{31}e + \frac{6}{31}$ |
| 64 | $[64, 2, -2]$ | $-\frac{21}{248}e^{6} + \frac{69}{248}e^{5} + \frac{147}{124}e^{4} - \frac{121}{31}e^{3} - \frac{43}{31}e^{2} + \frac{160}{31}e - \frac{115}{31}$ |
| 67 | $[67, 67, -w^{4} + 6w^{2} + w - 3]$ | $-\frac{5}{124}e^{6} + \frac{3}{31}e^{5} + \frac{101}{124}e^{4} - \frac{65}{31}e^{3} - \frac{112}{31}e^{2} + \frac{305}{31}e + \frac{146}{31}$ |
| 67 | $[67, 67, -2w^{4} + w^{3} + 10w^{2} - 6]$ | $\phantom{-}\frac{17}{124}e^{6} - \frac{4}{31}e^{5} - \frac{181}{62}e^{4} + \frac{171}{124}e^{3} + \frac{511}{31}e^{2} + \frac{17}{31}e - \frac{577}{31}$ |
| 73 | $[73, 73, w^{5} - 5w^{3} - 2w^{2} + 2w - 2]$ | $\phantom{-}\frac{7}{62}e^{6} - \frac{15}{124}e^{5} - \frac{289}{124}e^{4} + \frac{58}{31}e^{3} + \frac{326}{31}e^{2} - \frac{141}{31}e - \frac{12}{31}$ |
| 73 | $[73, 73, -w^{5} - w^{4} + 7w^{3} + 6w^{2} - 8w - 2]$ | $\phantom{-}\frac{5}{124}e^{6} - \frac{3}{31}e^{5} - \frac{39}{124}e^{4} + \frac{37}{62}e^{3} - \frac{105}{31}e^{2} + \frac{129}{31}e + \frac{412}{31}$ |
| 79 | $[79, 79, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 5w - 1]$ | $-\frac{11}{124}e^{6} + \frac{7}{62}e^{5} + \frac{77}{62}e^{4} - \frac{107}{124}e^{3} - \frac{48}{31}e^{2} - \frac{42}{31}e - \frac{119}{31}$ |
| 83 | $[83, 83, 2w^{5} - 11w^{3} - 4w^{2} + 6w]$ | $-\frac{7}{124}e^{6} + \frac{23}{124}e^{5} + \frac{40}{31}e^{4} - \frac{151}{62}e^{3} - \frac{256}{31}e^{2} - \frac{7}{31}e + \frac{192}{31}$ |
| 89 | $[89, 89, -2w^{5} + 11w^{3} + 4w^{2} - 7w - 2]$ | $-\frac{13}{124}e^{6} + \frac{25}{124}e^{5} + \frac{61}{31}e^{4} - \frac{183}{62}e^{3} - \frac{285}{31}e^{2} + \frac{235}{31}e + \frac{392}{31}$ |
| 97 | $[97, 97, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 2w - 2]$ | $-\frac{19}{124}e^{6} + \frac{27}{124}e^{5} + \frac{195}{62}e^{4} - \frac{92}{31}e^{3} - \frac{500}{31}e^{2} + \frac{198}{31}e + \frac{406}{31}$ |
| 97 | $[97, 97, w^{5} - w^{4} - 6w^{3} + 3w^{2} + 7w - 1]$ | $\phantom{-}\frac{7}{62}e^{6} - \frac{23}{62}e^{5} - \frac{129}{62}e^{4} + \frac{333}{62}e^{3} + \frac{295}{31}e^{2} - \frac{327}{31}e - \frac{198}{31}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, w^{5} - w^{4} - 5w^{3} + 2w^{2} + 4w]$ | $1$ |