Properties

Label 2.2.232.1-9.1-l
Base field \(\Q(\sqrt{58}) \)
Weight $[2, 2]$
Level norm $9$
Level $[9, 3, 3]$
Dimension $15$
CM no
Base change yes

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Base field \(\Q(\sqrt{58}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 58\); narrow class number \(2\) and class number \(2\).

Form

Weight: $[2, 2]$
Level: $[9, 3, 3]$
Dimension: $15$
CM: no
Base change: yes
Newspace dimension: $74$

Hecke eigenvalues ($q$-expansion)

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

\(x^{15} - 31x^{13} - x^{12} + 386x^{11} + 23x^{10} - 2462x^{9} - 204x^{8} + 8492x^{7} + 916x^{6} - 15320x^{5} - 2284x^{4} + 12648x^{3} + 2768x^{2} - 3328x - 768\)

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Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}e$
3 $[3, 3, w + 1]$ $-1$
3 $[3, 3, w + 2]$ $-1$
7 $[7, 7, -2w + 15]$ $...$
7 $[7, 7, -2w - 15]$ $...$
11 $[11, 11, w + 5]$ $...$
11 $[11, 11, w + 6]$ $...$
19 $[19, 19, w + 1]$ $...$
19 $[19, 19, w + 18]$ $...$
23 $[23, 23, w + 9]$ $...$
23 $[23, 23, -w + 9]$ $...$
25 $[25, 5, 5]$ $...$
29 $[29, 29, w]$ $...$
37 $[37, 37, w + 13]$ $...$
37 $[37, 37, w + 24]$ $...$
43 $[43, 43, w + 12]$ $...$
43 $[43, 43, w + 31]$ $...$
61 $[61, 61, w + 27]$ $...$
61 $[61, 61, w + 34]$ $...$
71 $[71, 71, 12w - 91]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w + 1]$ $1$
$3$ $[3, 3, w + 2]$ $1$