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 | $[3, 3, w + 1]$ | $-3e^{6} - 2e^{5} + 35e^{4} + 15e^{3} - 120e^{2} - 26e + 114$ |
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 | $[11, 11, w + 5]$ | $\phantom{-}7e^{6} + 4e^{5} - 83e^{4} - 30e^{3} + 290e^{2} + 52e - 282$ |
11 | $[11, 11, w + 6]$ | $\phantom{-}e^{4} + e^{3} - 7e^{2} - 4e + 7$ |
19 | $[19, 19, w + 1]$ | $\phantom{-}3e^{6} + 2e^{5} - 36e^{4} - 16e^{3} + 127e^{2} + 30e - 121$ |
19 | $[19, 19, w + 18]$ | $-9e^{6} - 5e^{5} + 108e^{4} + 37e^{3} - 382e^{2} - 64e + 374$ |
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 | $[29, 29, w]$ | $-e^{6} + 13e^{4} - 50e^{2} + 55$ |
37 | $[37, 37, w + 13]$ | $-5e^{6} - 3e^{5} + 60e^{4} + 23e^{3} - 215e^{2} - 42e + 214$ |
37 | $[37, 37, w + 24]$ | $\phantom{-}5e^{6} + 3e^{5} - 61e^{4} - 23e^{3} + 223e^{2} + 40e - 226$ |
43 | $[43, 43, w + 12]$ | $\phantom{-}10e^{6} + 6e^{5} - 120e^{4} - 46e^{3} + 424e^{2} + 81e - 411$ |
43 | $[43, 43, w + 31]$ | $-13e^{6} - 8e^{5} + 154e^{4} + 60e^{3} - 538e^{2} - 102e + 524$ |
61 | $[61, 61, w + 27]$ | $\phantom{-}11e^{6} + 7e^{5} - 129e^{4} - 53e^{3} + 444e^{2} + 91e - 423$ |
61 | $[61, 61, w + 34]$ | $\phantom{-}3e^{6} + e^{5} - 38e^{4} - 8e^{3} + 142e^{2} + 14e - 148$ |
71 | $[71, 71, 12w - 91]$ | $-6e^{6} - 5e^{5} + 70e^{4} + 39e^{3} - 239e^{2} - 64e + 219$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w + 2]$ | $-1$ |