Base field 6.6.1134389.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 4x^{4} + 6x^{3} + 4x^{2} - 3x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[37, 37, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - w + 3]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 33x^{4} + 288x^{2} - 400\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w^{2} - w - 2]$ | $\phantom{-}e$ |
| 13 | $[13, 13, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $-\frac{1}{30}e^{5} + \frac{23}{30}e^{3} - \frac{44}{15}e$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 3w]$ | $-\frac{1}{120}e^{5} + \frac{53}{120}e^{3} - \frac{127}{30}e$ |
| 19 | $[19, 19, w^{3} - w^{2} - 3w + 1]$ | $-\frac{1}{120}e^{5} - \frac{7}{120}e^{3} + \frac{64}{15}e$ |
| 19 | $[19, 19, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ | $\phantom{-}\frac{1}{12}e^{4} - \frac{17}{12}e^{2} - \frac{8}{3}$ |
| 23 | $[23, 23, -w^{4} + 2w^{3} + 3w^{2} - 3w - 2]$ | $\phantom{-}\frac{1}{30}e^{5} - \frac{23}{30}e^{3} + \frac{44}{15}e$ |
| 31 | $[31, 31, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w - 1]$ | $\phantom{-}\frac{1}{30}e^{5} - \frac{23}{30}e^{3} + \frac{59}{15}e$ |
| 37 | $[37, 37, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - w + 3]$ | $-1$ |
| 37 | $[37, 37, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 1]$ | $\phantom{-}0$ |
| 47 | $[47, 47, -w^{3} + 2w^{2} + w - 3]$ | $-\frac{1}{6}e^{4} + \frac{17}{6}e^{2} - \frac{5}{3}$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{1}{12}e^{4} - \frac{29}{12}e^{2} + \frac{34}{3}$ |
| 67 | $[67, 67, 2w - 1]$ | $\phantom{-}\frac{1}{6}e^{4} - \frac{23}{6}e^{2} + \frac{32}{3}$ |
| 79 | $[79, 79, w^{4} - w^{3} - 4w^{2} + 2w]$ | $\phantom{-}\frac{1}{120}e^{5} + \frac{7}{120}e^{3} - \frac{19}{15}e$ |
| 79 | $[79, 79, -w^{5} + 2w^{4} + 3w^{3} - 5w^{2} - w + 4]$ | $-\frac{1}{30}e^{5} + \frac{19}{15}e^{3} - \frac{373}{30}e$ |
| 97 | $[97, 97, w^{5} - 2w^{4} - 3w^{3} + 6w^{2} - 3]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{21}{4}e^{2} + 18$ |
| 97 | $[97, 97, w^{5} - 3w^{4} - 2w^{3} + 9w^{2} - 2w - 4]$ | $-\frac{1}{30}e^{5} + \frac{23}{30}e^{3} - \frac{29}{15}e$ |
| 101 | $[101, 101, w^{5} - 2w^{4} - 3w^{3} + 5w^{2} - w - 2]$ | $-\frac{1}{15}e^{5} + \frac{61}{30}e^{3} - \frac{431}{30}e$ |
| 101 | $[101, 101, w^{5} - 3w^{4} - 2w^{3} + 10w^{2} - w - 5]$ | $-\frac{7}{120}e^{5} + \frac{131}{120}e^{3} + \frac{11}{30}e$ |
| 103 | $[103, 103, 2w^{5} - 3w^{4} - 9w^{3} + 8w^{2} + 8w - 3]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{19}{2}e$ |
| 107 | $[107, 107, w^{2} - 2w - 3]$ | $\phantom{-}\frac{1}{6}e^{4} - \frac{29}{6}e^{2} + \frac{59}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $37$ | $[37,37,-w^{5}+3w^{4}+2w^{3}-8w^{2}-w+3]$ | $1$ |