Base field 3.3.1825.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x + 7\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[29, 29, -w^{2} - 2w + 4]$ |
| Dimension: | $50$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $84$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{50} - 206x^{48} + 19589x^{46} - 1142471x^{44} + 45802200x^{42} - 1340959236x^{40} + 29735844507x^{38} - 511307550762x^{36} + 6924198271826x^{34} - 74605806584465x^{32} + 643634570618433x^{30} - 4460684622000322x^{28} + 24853158682356447x^{26} - 111145484262354520x^{24} + 397421433485995408x^{22} - 1129096949223774464x^{20} + 2525966745242127688x^{18} - 4395891276174614558x^{16} + 5855577941512730856x^{14} - 5844052517368383808x^{12} + 4246503328103048684x^{10} - 2159129832401484792x^{8} + 724874712052191408x^{6} - 146570821590187904x^{4} + 15115625495302400x^{2} - 536087194560000\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w + 2]$ | $...$ |
| 7 | $[7, 7, w]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $...$ |
| 11 | $[11, 11, w + 2]$ | $...$ |
| 13 | $[13, 13, w + 1]$ | $...$ |
| 17 | $[17, 17, -w^{2} - w + 4]$ | $...$ |
| 23 | $[23, 23, -w^{2} + 6]$ | $...$ |
| 23 | $[23, 23, -w^{2} - w + 3]$ | $...$ |
| 23 | $[23, 23, -w + 4]$ | $...$ |
| 27 | $[27, 3, 3]$ | $...$ |
| 29 | $[29, 29, -w^{2} - 2w + 4]$ | $\phantom{-}1$ |
| 31 | $[31, 31, w^{2} - 10]$ | $...$ |
| 41 | $[41, 41, w + 4]$ | $...$ |
| 41 | $[41, 41, w^{2} - 5]$ | $...$ |
| 41 | $[41, 41, -2w - 5]$ | $...$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $...$ |
| 47 | $[47, 47, w^{2} - w - 9]$ | $...$ |
| 49 | $[49, 7, w^{2} - w - 8]$ | $...$ |
| 53 | $[53, 53, 2w^{2} + w - 12]$ | $...$ |
| 59 | $[59, 59, w^{2} - 3]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, -w^{2} - 2w + 4]$ | $-1$ |