Properties

Base field 4.4.17725.1
Weight [2, 2, 2, 2]
Level norm 9
Level $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$
Label 4.4.17725.1-9.1-a
Dimension 5
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 $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$
Label 4.4.17725.1-9.1-a
Dimension 5
Is CM no
Is base change no
Parent newspace dimension 13

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} \) \(\mathstrut +\mathstrut 4x^{4} \) \(\mathstrut -\mathstrut x^{3} \) \(\mathstrut -\mathstrut 16x^{2} \) \(\mathstrut -\mathstrut 14x \) \(\mathstrut -\mathstrut 1\)

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Norm Prime Eigenvalue
9 $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ $\phantom{-}1$
9 $[9, 3, -w^{3} + 8w + 8]$ $\phantom{-}e$
16 $[16, 2, 2]$ $\phantom{-}9e^{4} + 23e^{3} - 42e^{2} - 84e - 8$
19 $[19, 19, w + 1]$ $\phantom{-}4e^{4} + 9e^{3} - 22e^{2} - 33e + 5$
19 $[19, 19, -w^{2} + 6]$ $\phantom{-}6e^{4} + 17e^{3} - 25e^{2} - 64e - 12$
19 $[19, 19, -w^{2} + 2w + 5]$ $\phantom{-}e^{4} + 2e^{3} - 6e^{2} - 7e + 4$
19 $[19, 19, -w + 2]$ $-5e^{4} - 12e^{3} + 25e^{2} + 43e - 4$
25 $[25, 5, 2w^{2} - 2w - 13]$ $\phantom{-}2e^{4} + 5e^{3} - 10e^{2} - 17e + 1$
29 $[29, 29, -w^{2} + 9]$ $-e^{4} - 3e^{3} + 2e^{2} + 8e + 8$
29 $[29, 29, -w^{2} + 2w + 6]$ $\phantom{-}10e^{4} + 26e^{3} - 45e^{2} - 93e - 13$
29 $[29, 29, w^{2} - 7]$ $-3e^{4} - 7e^{3} + 15e^{2} + 23e - 5$
29 $[29, 29, -w^{2} + 2w + 8]$ $-8e^{4} - 21e^{3} + 37e^{2} + 78e + 3$
31 $[31, 31, -2w^{2} + w + 12]$ $-11e^{4} - 28e^{3} + 53e^{2} + 102e - 1$
31 $[31, 31, 2w^{2} - 3w - 11]$ $-4e^{4} - 9e^{3} + 22e^{2} + 29e - 7$
41 $[41, 41, -w]$ $-8e^{4} - 22e^{3} + 34e^{2} + 84e + 17$
41 $[41, 41, -w + 1]$ $-5e^{4} - 13e^{3} + 24e^{2} + 46e - 4$
49 $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ $\phantom{-}8e^{4} + 21e^{3} - 37e^{2} - 74e - 3$
49 $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ $-7e^{4} - 21e^{3} + 28e^{2} + 82e + 19$
61 $[61, 61, 2w^{2} - 3w - 14]$ $-6e^{4} - 16e^{3} + 25e^{2} + 57e + 5$
61 $[61, 61, 2w^{2} - w - 15]$ $\phantom{-}e^{3} + 4e^{2} - 2e - 13$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ $-1$