Base field \(\Q(\sqrt{46}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 46\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[7, 7, 4w - 27]$ |
| Dimension: | $14$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{14} - 3x^{13} - 15x^{12} + 48x^{11} + 79x^{10} - 289x^{9} - 154x^{8} + 805x^{7} - 8x^{6} - 1005x^{5} + 286x^{4} + 433x^{3} - 117x^{2} - 64x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, 23w - 156]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w - 7]$ | $...$ |
| 3 | $[3, 3, w - 7]$ | $...$ |
| 5 | $[5, 5, -9w + 61]$ | $...$ |
| 5 | $[5, 5, -9w - 61]$ | $...$ |
| 7 | $[7, 7, 4w - 27]$ | $\phantom{-}1$ |
| 7 | $[7, 7, 4w + 27]$ | $...$ |
| 23 | $[23, 23, 78w - 529]$ | $...$ |
| 37 | $[37, 37, -w - 3]$ | $...$ |
| 37 | $[37, 37, w - 3]$ | $...$ |
| 41 | $[41, 41, -2w + 15]$ | $...$ |
| 41 | $[41, 41, 2w + 15]$ | $...$ |
| 53 | $[53, 53, -3w - 19]$ | $...$ |
| 53 | $[53, 53, 3w - 19]$ | $...$ |
| 59 | $[59, 59, 11w - 75]$ | $...$ |
| 59 | $[59, 59, -11w - 75]$ | $...$ |
| 61 | $[61, 61, -5w + 33]$ | $...$ |
| 61 | $[61, 61, 5w + 33]$ | $...$ |
| 73 | $[73, 73, -24w - 163]$ | $...$ |
| 73 | $[73, 73, -24w + 163]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, 4w - 27]$ | $-1$ |