Properties

Base field 4.4.17725.1
Weight [2, 2, 2, 2]
Level norm 19
Level $[19,19,-w^{2} + 2w + 5]$
Label 4.4.17725.1-19.3-b
Dimension 12
CM no
Base change no

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Base field 4.4.17725.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 12x^{2} + 13x + 41\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[19,19,-w^{2} + 2w + 5]$
Label 4.4.17725.1-19.3-b
Dimension 12
Is CM no
Is base change no
Parent newspace dimension 32

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{12} \) \(\mathstrut +\mathstrut 2x^{11} \) \(\mathstrut -\mathstrut 56x^{10} \) \(\mathstrut -\mathstrut 97x^{9} \) \(\mathstrut +\mathstrut 1130x^{8} \) \(\mathstrut +\mathstrut 1649x^{7} \) \(\mathstrut -\mathstrut 9868x^{6} \) \(\mathstrut -\mathstrut 11978x^{5} \) \(\mathstrut +\mathstrut 35133x^{4} \) \(\mathstrut +\mathstrut 38543x^{3} \) \(\mathstrut -\mathstrut 38960x^{2} \) \(\mathstrut -\mathstrut 47327x \) \(\mathstrut -\mathstrut 8797\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ $\phantom{-}e$
9 $[9, 3, -w^{3} + 8w + 8]$ $...$
16 $[16, 2, 2]$ $...$
19 $[19, 19, w + 1]$ $...$
19 $[19, 19, -w^{2} + 6]$ $...$
19 $[19, 19, -w^{2} + 2w + 5]$ $\phantom{-}1$
19 $[19, 19, -w + 2]$ $...$
25 $[25, 5, 2w^{2} - 2w - 13]$ $...$
29 $[29, 29, -w^{2} + 9]$ $...$
29 $[29, 29, -w^{2} + 2w + 6]$ $...$
29 $[29, 29, w^{2} - 7]$ $...$
29 $[29, 29, -w^{2} + 2w + 8]$ $...$
31 $[31, 31, -2w^{2} + w + 12]$ $...$
31 $[31, 31, 2w^{2} - 3w - 11]$ $...$
41 $[41, 41, -w]$ $...$
41 $[41, 41, -w + 1]$ $...$
49 $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ $...$
49 $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ $...$
61 $[61, 61, 2w^{2} - 3w - 14]$ $...$
61 $[61, 61, 2w^{2} - w - 15]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
19 $[19,19,-w^{2} + 2w + 5]$ $-1$