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-c
Dimension 19
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-c
Dimension 19
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:
\(x^{19} \) \(\mathstrut -\mathstrut 10x^{18} \) \(\mathstrut -\mathstrut 31x^{17} \) \(\mathstrut +\mathstrut 557x^{16} \) \(\mathstrut -\mathstrut 299x^{15} \) \(\mathstrut -\mathstrut 10638x^{14} \) \(\mathstrut +\mathstrut 15837x^{13} \) \(\mathstrut +\mathstrut 92616x^{12} \) \(\mathstrut -\mathstrut 145469x^{11} \) \(\mathstrut -\mathstrut 470115x^{10} \) \(\mathstrut +\mathstrut 540469x^{9} \) \(\mathstrut +\mathstrut 1470025x^{8} \) \(\mathstrut -\mathstrut 760970x^{7} \) \(\mathstrut -\mathstrut 2531686x^{6} \) \(\mathstrut +\mathstrut 21836x^{5} \) \(\mathstrut +\mathstrut 1999540x^{4} \) \(\mathstrut +\mathstrut 624949x^{3} \) \(\mathstrut -\mathstrut 462855x^{2} \) \(\mathstrut -\mathstrut 207947x \) \(\mathstrut +\mathstrut 886\)

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