Properties

Label 2.2.157.1-11.1-b
Base field \(\Q(\sqrt{157}) \)
Weight $[2, 2]$
Level norm $11$
Level $[11, 11, -3w - 17]$
Dimension $17$
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: $[11, 11, -3w - 17]$
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 $[67, 67, 3w - 22]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$11$ $[11, 11, -3w - 17]$ $1$