Base field \(\Q(\sqrt{305}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 76\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[7, 7, w + 2]$ |
| Dimension: | $40$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $160$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{40} - 10x^{39} - 11x^{38} + 422x^{37} - 715x^{36} - 7574x^{35} + 23950x^{34} + 72347x^{33} - 357292x^{32} - 339984x^{31} + 3249778x^{30} - 180864x^{29} - 19824156x^{28} + 13892601x^{27} + 84156991x^{26} - 102416693x^{25} - 249952936x^{24} + 436224332x^{23} + 504484109x^{22} - 1252557065x^{21} - 618154040x^{20} + 2534280592x^{19} + 218633196x^{18} - 3648854489x^{17} + 705129588x^{16} + 3700784293x^{15} - 1499336791x^{14} - 2564347960x^{13} + 1508973647x^{12} + 1138412832x^{11} - 897866034x^{10} - 278539949x^{9} + 316156339x^{8} + 19174925x^{7} - 60303202x^{6} + 5194142x^{5} + 5134397x^{4} - 819142x^{3} - 147517x^{2} + 27557x + 335\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $...$ |
| 5 | $[5, 5, -4w + 37]$ | $...$ |
| 7 | $[7, 7, w + 2]$ | $-1$ |
| 7 | $[7, 7, w + 4]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 17 | $[17, 17, w + 6]$ | $...$ |
| 17 | $[17, 17, w + 10]$ | $...$ |
| 19 | $[19, 19, -2w + 19]$ | $...$ |
| 19 | $[19, 19, -2w - 17]$ | $...$ |
| 23 | $[23, 23, w + 5]$ | $...$ |
| 23 | $[23, 23, w + 17]$ | $...$ |
| 37 | $[37, 37, w + 1]$ | $...$ |
| 37 | $[37, 37, w + 35]$ | $...$ |
| 41 | $[41, 41, -22w + 203]$ | $...$ |
| 41 | $[41, 41, -6w + 55]$ | $...$ |
| 43 | $[43, 43, w + 20]$ | $...$ |
| 43 | $[43, 43, w + 22]$ | $...$ |
| 53 | $[53, 53, w + 13]$ | $...$ |
| 53 | $[53, 53, w + 39]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w + 2]$ | $1$ |