Base field \(\Q(\sqrt{157}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 39\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[12, 6, 2w + 12]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 3x^{5} - 10x^{4} + 33x^{3} - 8x^{2} - 8x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 6]$ | $-1$ |
| 3 | $[3, 3, -w + 7]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $-1$ |
| 11 | $[11, 11, -3w - 17]$ | $\phantom{-}12e^{5} - 39e^{4} - 111e^{3} + 425e^{2} - 194e - 58$ |
| 11 | $[11, 11, 3w - 20]$ | $-3e^{5} + 10e^{4} + 27e^{3} - 109e^{2} + 57e + 14$ |
| 13 | $[13, 13, 2w - 13]$ | $\phantom{-}4e^{5} - 13e^{4} - 37e^{3} + 141e^{2} - 65e - 15$ |
| 13 | $[13, 13, 2w + 11]$ | $\phantom{-}4e^{5} - 13e^{4} - 37e^{3} + 142e^{2} - 63e - 23$ |
| 17 | $[17, 17, w + 7]$ | $\phantom{-}e^{3} - 11e + 4$ |
| 17 | $[17, 17, -w + 8]$ | $\phantom{-}19e^{5} - 61e^{4} - 178e^{3} + 664e^{2} - 284e - 91$ |
| 19 | $[19, 19, -w - 4]$ | $\phantom{-}2e^{5} - 6e^{4} - 19e^{3} + 66e^{2} - 27e - 11$ |
| 19 | $[19, 19, -w + 5]$ | $\phantom{-}17e^{5} - 55e^{4} - 158e^{3} + 599e^{2} - 266e - 83$ |
| 25 | $[25, 5, 5]$ | $\phantom{-}6e^{5} - 19e^{4} - 56e^{3} + 207e^{2} - 89e - 30$ |
| 31 | $[31, 31, -6w - 35]$ | $\phantom{-}26e^{5} - 83e^{4} - 243e^{3} + 904e^{2} - 393e - 123$ |
| 31 | $[31, 31, -6w + 41]$ | $\phantom{-}7e^{5} - 22e^{4} - 65e^{3} + 239e^{2} - 108e - 28$ |
| 37 | $[37, 37, -w - 1]$ | $\phantom{-}17e^{5} - 55e^{4} - 158e^{3} + 600e^{2} - 268e - 86$ |
| 37 | $[37, 37, w - 2]$ | $\phantom{-}17e^{5} - 55e^{4} - 159e^{3} + 599e^{2} - 256e - 86$ |
| 47 | $[47, 47, 3w + 16]$ | $-21e^{5} + 68e^{4} + 195e^{3} - 741e^{2} + 330e + 104$ |
| 47 | $[47, 47, -3w + 19]$ | $\phantom{-}13e^{5} - 42e^{4} - 122e^{3} + 457e^{2} - 193e - 59$ |
| 49 | $[49, 7, -7]$ | $-5e^{5} + 16e^{4} + 46e^{3} - 175e^{2} + 83e + 21$ |
| 67 | $[67, 67, 3w - 22]$ | $-31e^{5} + 99e^{4} + 289e^{3} - 1078e^{2} + 475e + 150$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 6]$ | $1$ |
| $4$ | $[4, 2, 2]$ | $1$ |