Properties

Label 2.2.197.1-49.2-g
Base field \(\Q(\sqrt{197}) \)
Weight $[2, 2]$
Level norm $49$
Level $[49, 49, w]$
Dimension $13$
CM no
Base change no

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Base field \(\Q(\sqrt{197}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 49\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[49, 49, w]$
Dimension: $13$
CM: no
Base change: no
Newspace dimension: $165$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{13} + 6x^{12} - 10x^{11} - 110x^{10} - 32x^{9} + 709x^{8} + 624x^{7} - 1981x^{6} - 2292x^{5} + 2289x^{4} + 3181x^{3} - 662x^{2} - 1476x - 259\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $\phantom{-}e$
7 $[7, 7, w - 7]$ $\phantom{-}0$
7 $[7, 7, w + 6]$ $...$
9 $[9, 3, 3]$ $...$
19 $[19, 19, w + 5]$ $...$
19 $[19, 19, w - 6]$ $...$
23 $[23, 23, w + 8]$ $...$
23 $[23, 23, -w + 9]$ $...$
25 $[25, 5, 5]$ $...$
29 $[29, 29, -w - 4]$ $...$
29 $[29, 29, w - 5]$ $...$
37 $[37, 37, -w - 3]$ $...$
37 $[37, 37, w - 4]$ $...$
41 $[41, 41, -w - 9]$ $...$
41 $[41, 41, w - 10]$ $...$
43 $[43, 43, -w - 2]$ $...$
43 $[43, 43, w - 3]$ $...$
47 $[47, 47, -w - 1]$ $...$
47 $[47, 47, w - 2]$ $...$
53 $[53, 53, 2w - 13]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$7$ $[7, 7, w - 7]$ $-1$