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: | $[9,9,-14w + 95]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $29$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 18x^{4} + 50x^{2} - 38\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, 23w - 156]$ | $-3e^{4} + 49e^{2} - 71$ |
| 3 | $[3, 3, -w - 7]$ | $\phantom{-}3e^{4} - 49e^{2} + 70$ |
| 3 | $[3, 3, w - 7]$ | $\phantom{-}0$ |
| 5 | $[5, 5, -9w + 61]$ | $\phantom{-}2e^{5} - 33e^{3} + 50e$ |
| 5 | $[5, 5, -9w - 61]$ | $\phantom{-}e$ |
| 7 | $[7, 7, 4w - 27]$ | $-5e^{5} + 82e^{3} - 118e$ |
| 7 | $[7, 7, 4w + 27]$ | $-e$ |
| 23 | $[23, 23, 78w - 529]$ | $\phantom{-}5e^{5} - 82e^{3} + 117e$ |
| 37 | $[37, 37, -w - 3]$ | $-5e^{5} + 82e^{3} - 119e$ |
| 37 | $[37, 37, w - 3]$ | $-e^{5} + 17e^{3} - 33e$ |
| 41 | $[41, 41, -2w + 15]$ | $-10e^{4} + 163e^{2} - 232$ |
| 41 | $[41, 41, 2w + 15]$ | $\phantom{-}5e^{4} - 82e^{2} + 116$ |
| 53 | $[53, 53, -3w - 19]$ | $\phantom{-}13e^{5} - 213e^{3} + 306e$ |
| 53 | $[53, 53, 3w - 19]$ | $-11e^{5} + 180e^{3} - 255e$ |
| 59 | $[59, 59, 11w - 75]$ | $\phantom{-}13e^{4} - 214e^{2} + 310$ |
| 59 | $[59, 59, -11w - 75]$ | $\phantom{-}11e^{4} - 180e^{2} + 260$ |
| 61 | $[61, 61, -5w + 33]$ | $\phantom{-}8e^{5} - 131e^{3} + 186e$ |
| 61 | $[61, 61, 5w + 33]$ | $\phantom{-}9e^{5} - 147e^{3} + 206e$ |
| 73 | $[73, 73, -24w - 163]$ | $-23e^{4} + 376e^{2} - 542$ |
| 73 | $[73, 73, -24w + 163]$ | $-7e^{4} + 116e^{2} - 178$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3,3,w - 7]$ | $-1$ |