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: | $[7,7,-w + 3]$ |
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 | $[2, 2, w]$ | $...$ |
2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
5 | $[5, 5, -4w + 37]$ | $...$ |
7 | $[7, 7, w + 2]$ | $...$ |
7 | $[7, 7, w + 4]$ | $\phantom{-}1$ |
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 |
---|---|---|
$7$ | $[7,7,-w + 3]$ | $-1$ |