Base field \(\Q(\sqrt{58}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 58\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9, 9, -w + 7]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $80$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 2x^{6} - 11x^{5} + 21x^{4} + 35x^{3} - 65x^{2} - 29x + 55\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}3e^{6} - 2e^{5} - 35e^{4} + 15e^{3} + 120e^{2} - 26e - 114$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}0$ |
| 7 | $[7, 7, -2w + 15]$ | $\phantom{-}3e^{6} - 2e^{5} - 36e^{4} + 16e^{3} + 127e^{2} - 30e - 123$ |
| 7 | $[7, 7, -2w - 15]$ | $-e^{6} + e^{5} + 12e^{4} - 8e^{3} - 43e^{2} + 14e + 42$ |
| 11 | $[11, 11, w + 5]$ | $-7e^{6} + 4e^{5} + 83e^{4} - 30e^{3} - 290e^{2} + 52e + 282$ |
| 11 | $[11, 11, w + 6]$ | $-e^{4} + e^{3} + 7e^{2} - 4e - 7$ |
| 19 | $[19, 19, w + 1]$ | $-3e^{6} + 2e^{5} + 36e^{4} - 16e^{3} - 127e^{2} + 30e + 121$ |
| 19 | $[19, 19, w + 18]$ | $\phantom{-}9e^{6} - 5e^{5} - 108e^{4} + 37e^{3} + 382e^{2} - 64e - 374$ |
| 23 | $[23, 23, w + 9]$ | $-5e^{6} + 3e^{5} + 60e^{4} - 24e^{3} - 212e^{2} + 47e + 205$ |
| 23 | $[23, 23, -w + 9]$ | $\phantom{-}9e^{6} - 6e^{5} - 107e^{4} + 45e^{3} + 377e^{2} - 76e - 370$ |
| 25 | $[25, 5, 5]$ | $-6e^{6} + 4e^{5} + 71e^{4} - 31e^{3} - 249e^{2} + 55e + 243$ |
| 29 | $[29, 29, w]$ | $\phantom{-}e^{6} - 13e^{4} + 50e^{2} - 55$ |
| 37 | $[37, 37, w + 13]$ | $\phantom{-}5e^{6} - 3e^{5} - 60e^{4} + 23e^{3} + 215e^{2} - 42e - 214$ |
| 37 | $[37, 37, w + 24]$ | $-5e^{6} + 3e^{5} + 61e^{4} - 23e^{3} - 223e^{2} + 40e + 226$ |
| 43 | $[43, 43, w + 12]$ | $-10e^{6} + 6e^{5} + 120e^{4} - 46e^{3} - 424e^{2} + 81e + 411$ |
| 43 | $[43, 43, w + 31]$ | $\phantom{-}13e^{6} - 8e^{5} - 154e^{4} + 60e^{3} + 538e^{2} - 102e - 524$ |
| 61 | $[61, 61, w + 27]$ | $-11e^{6} + 7e^{5} + 129e^{4} - 53e^{3} - 444e^{2} + 91e + 423$ |
| 61 | $[61, 61, w + 34]$ | $-3e^{6} + e^{5} + 38e^{4} - 8e^{3} - 142e^{2} + 14e + 148$ |
| 71 | $[71, 71, 12w - 91]$ | $-6e^{6} + 5e^{5} + 70e^{4} - 39e^{3} - 239e^{2} + 64e + 219$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 2]$ | $-1$ |