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: | $[17, 17, w + 7]$ |
Dimension: | $29$ |
CM: | no |
Base change: | no |
Newspace dimension: | $53$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{29} - 4x^{28} - 49x^{27} + 210x^{26} + 1000x^{25} - 4772x^{24} - 10806x^{23} + 61669x^{22} + 62360x^{21} - 500303x^{20} - 125961x^{19} + 2650036x^{18} - 707982x^{17} - 9218198x^{16} + 6098918x^{15} + 20572597x^{14} - 20729688x^{13} - 27646863x^{12} + 38713479x^{11} + 19183544x^{10} - 40826878x^{9} - 3628065x^{8} + 23489360x^{7} - 2036489x^{6} - 7424885x^{5} + 964907x^{4} + 1252343x^{3} - 91681x^{2} - 92008x - 5816\) |
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 | $[13, 13, 2w + 11]$ | $...$ |
17 | $[17, 17, w + 7]$ | $-1$ |
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 |
---|---|---|
$17$ | $[17, 17, w + 7]$ | $1$ |