Properties

Label 2.2.157.1-17.1-c
Base field \(\Q(\sqrt{157}) \)
Weight $[2, 2]$
Level norm $17$
Level $[17, 17, w + 7]$
Dimension $29$
CM no
Base change no

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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 $[67, 67, 3w - 22]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$17$ $[17, 17, w + 7]$ $1$