Base field \(\Q(\sqrt{229}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 57\); narrow class number \(3\) and class number \(3\).
Form
Weight: | $[2, 2]$ |
Level: | $[11,11,-w + 2]$ |
Dimension: | $35$ |
CM: | no |
Base change: | no |
Newspace dimension: | $186$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{35} - 10x^{34} - 19x^{33} + 490x^{32} - 553x^{31} - 10391x^{30} + 25391x^{29} + 123363x^{28} - 441031x^{27} - 867039x^{26} + 4530403x^{25} + 3197287x^{24} - 30860046x^{23} + 450259x^{22} + 145792455x^{21} - 73272536x^{20} - 484403785x^{19} + 430418719x^{18} + 1121320228x^{17} - 1410842338x^{16} - 1736560733x^{15} + 2995725440x^{14} + 1600576284x^{13} - 4225897995x^{12} - 483137204x^{11} + 3875321675x^{10} - 644093461x^{9} - 2165838756x^{8} + 803276922x^{7} + 641819817x^{6} - 351235625x^{5} - 69661322x^{4} + 57993125x^{3} - 1565705x^{2} - 2064580x + 181300\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $...$ |
3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
4 | $[4, 2, 2]$ | $...$ |
5 | $[5, 5, w + 1]$ | $...$ |
5 | $[5, 5, w + 3]$ | $...$ |
11 | $[11, 11, w + 1]$ | $...$ |
11 | $[11, 11, w + 9]$ | $-1$ |
17 | $[17, 17, w + 2]$ | $...$ |
17 | $[17, 17, w + 14]$ | $...$ |
19 | $[19, 19, w]$ | $...$ |
19 | $[19, 19, w + 18]$ | $...$ |
37 | $[37, 37, -w - 4]$ | $...$ |
37 | $[37, 37, w - 5]$ | $...$ |
43 | $[43, 43, w + 16]$ | $...$ |
43 | $[43, 43, w + 26]$ | $...$ |
49 | $[49, 7, -7]$ | $...$ |
53 | $[53, 53, -w - 10]$ | $...$ |
53 | $[53, 53, w - 11]$ | $...$ |
61 | $[61, 61, w + 15]$ | $...$ |
61 | $[61, 61, w + 45]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$11$ | $[11,11,-w + 2]$ | $1$ |