Base field \(\Q(\sqrt{91}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 91\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[3, 3, -2w + 19]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $60$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 15x^{10} + 79x^{8} - 170x^{6} + 129x^{4} - 35x^{2} + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -2w + 19]$ | $-1$ |
| 3 | $[3, 3, -2w - 19]$ | $\phantom{-}2e^{10} - 29e^{8} + 143e^{6} - 263e^{4} + 110e^{2} - 4$ |
| 5 | $[5, 5, w + 1]$ | $\phantom{-}9e^{11} - 130e^{9} + 639e^{7} - 1177e^{5} + 511e^{3} - 28e$ |
| 5 | $[5, 5, w + 4]$ | $-4e^{11} + 58e^{9} - 288e^{7} + 547e^{5} - 278e^{3} + 33e$ |
| 7 | $[7, 7, w]$ | $\phantom{-}2e^{11} - 29e^{9} + 143e^{7} - 263e^{5} + 109e^{3} - e$ |
| 11 | $[11, 11, w + 5]$ | $\phantom{-}10e^{11} - 144e^{9} + 704e^{7} - 1281e^{5} + 524e^{3} - 13e$ |
| 11 | $[11, 11, w + 6]$ | $-e^{11} + 14e^{9} - 66e^{7} + 114e^{5} - 39e^{3} - 6e$ |
| 13 | $[13, 13, w]$ | $-6e^{11} + 87e^{9} - 430e^{7} + 800e^{5} - 361e^{3} + 27e$ |
| 29 | $[29, 29, -5w + 48]$ | $\phantom{-}13e^{10} - 188e^{8} + 927e^{6} - 1723e^{4} + 783e^{2} - 58$ |
| 29 | $[29, 29, -5w - 48]$ | $\phantom{-}8e^{10} - 117e^{8} + 584e^{6} - 1098e^{4} + 499e^{2} - 32$ |
| 41 | $[41, 41, w + 3]$ | $\phantom{-}27e^{11} - 392e^{9} + 1942e^{7} - 3632e^{5} + 1674e^{3} - 122e$ |
| 41 | $[41, 41, w + 38]$ | $\phantom{-}e^{9} - 15e^{7} + 75e^{5} - 134e^{3} + 45e$ |
| 53 | $[53, 53, -w - 12]$ | $\phantom{-}6e^{10} - 87e^{8} + 429e^{6} - 792e^{4} + 347e^{2} - 26$ |
| 53 | $[53, 53, w - 12]$ | $\phantom{-}12e^{10} - 173e^{8} + 850e^{6} - 1575e^{4} + 718e^{2} - 54$ |
| 67 | $[67, 67, w + 15]$ | $-35e^{11} + 508e^{9} - 2518e^{7} + 4726e^{5} - 2231e^{3} + 192e$ |
| 67 | $[67, 67, w + 52]$ | $\phantom{-}23e^{11} - 334e^{9} + 1656e^{7} - 3107e^{5} + 1463e^{3} - 130e$ |
| 71 | $[71, 71, w + 34]$ | $\phantom{-}9e^{11} - 130e^{9} + 639e^{7} - 1177e^{5} + 508e^{3} - 12e$ |
| 71 | $[71, 71, w + 37]$ | $\phantom{-}34e^{11} - 492e^{9} + 2424e^{7} - 4480e^{5} + 1964e^{3} - 117e$ |
| 73 | $[73, 73, w + 23]$ | $-6e^{11} + 86e^{9} - 416e^{7} + 733e^{5} - 240e^{3} - 22e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -2w + 19]$ | $1$ |