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: | $[13,13,-2w - 11]$ |
| Dimension: | $23$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $44$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{23} - 2x^{22} - 53x^{21} + 102x^{20} + 1211x^{19} - 2207x^{18} - 15684x^{17} + 26463x^{16} + 127465x^{15} - 192791x^{14} - 680274x^{13} + 880397x^{12} + 2423734x^{11} - 2506491x^{10} - 5731973x^{9} + 4259090x^{8} + 8733548x^{7} - 3850250x^{6} - 8028594x^{5} + 1235189x^{4} + 3856635x^{3} + 339195x^{2} - 655130x - 154628\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 6]$ | $...$ |
| 3 | $[3, 3, -w + 7]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $...$ |
| 11 | $[11, 11, -3w - 17]$ | $...$ |
| 11 | $[11, 11, 3w - 20]$ | $...$ |
| 13 | $[13, 13, 2w - 13]$ | $...$ |
| 13 | $[13, 13, 2w + 11]$ | $-1$ |
| 17 | $[17, 17, w + 7]$ | $...$ |
| 17 | $[17, 17, -w + 8]$ | $...$ |
| 19 | $[19, 19, -w - 4]$ | $...$ |
| 19 | $[19, 19, -w + 5]$ | $...$ |
| 25 | $[25, 5, 5]$ | $...$ |
| 31 | $[31, 31, -6w - 35]$ | $...$ |
| 31 | $[31, 31, -6w + 41]$ | $...$ |
| 37 | $[37, 37, -w - 1]$ | $...$ |
| 37 | $[37, 37, w - 2]$ | $...$ |
| 47 | $[47, 47, 3w + 16]$ | $...$ |
| 47 | $[47, 47, -3w + 19]$ | $...$ |
| 49 | $[49, 7, -7]$ | $...$ |
| 67 | $[67, 67, 3w - 22]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13,13,-2w - 11]$ | $1$ |