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: | $[11, 11, -3w - 17]$ |
Dimension: | $17$ |
CM: | no |
Base change: | no |
Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{17} - 2x^{16} - 37x^{15} + 72x^{14} + 555x^{13} - 1033x^{12} - 4393x^{11} + 7592x^{10} + 20100x^{9} - 30534x^{8} - 55106x^{7} + 65879x^{6} + 91530x^{5} - 67293x^{4} - 89223x^{3} + 19019x^{2} + 39557x + 9277\) |
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 | $[11, 11, -3w - 17]$ | $-1$ |
11 | $[11, 11, 3w - 20]$ | $...$ |
13 | $[13, 13, 2w - 13]$ | $...$ |
13 | $[13, 13, 2w + 11]$ | $...$ |
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 |
---|---|---|
$11$ | $[11, 11, -3w - 17]$ | $1$ |