Properties

Base field 4.4.9248.1
Weight [2, 2, 2, 2]
Level norm 13
Level $[13, 13, -w^{2} + w + 3]$
Label 4.4.9248.1-13.1-a
Dimension 7
CM no
Base change no

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Base field 4.4.9248.1

Generator \(w\), with minimal polynomial \(x^{4} - 5x^{2} + 2\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[13, 13, -w^{2} + w + 3]$
Label 4.4.9248.1-13.1-a
Dimension 7
Is CM no
Is base change no
Parent newspace dimension 14

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{7} \) \(\mathstrut -\mathstrut 5x^{6} \) \(\mathstrut +\mathstrut 2x^{5} \) \(\mathstrut +\mathstrut 22x^{4} \) \(\mathstrut -\mathstrut 27x^{3} \) \(\mathstrut -\mathstrut 13x^{2} \) \(\mathstrut +\mathstrut 25x \) \(\mathstrut -\mathstrut 4\)

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Norm Prime Eigenvalue
2 $[2, 2, w]$ $-e^{6} + 3e^{5} + 4e^{4} - 15e^{3} - e^{2} + 15e - 1$
2 $[2, 2, w + 1]$ $\phantom{-}e$
13 $[13, 13, -w^{2} + w + 3]$ $-1$
13 $[13, 13, w^{2} + w - 3]$ $\phantom{-}e^{5} - 2e^{4} - 5e^{3} + 9e^{2} + 4e - 4$
19 $[19, 19, -w^{3} + 3w + 1]$ $-2e^{5} + 3e^{4} + 12e^{3} - 13e^{2} - 15e + 10$
19 $[19, 19, -w^{3} + 3w - 1]$ $-e^{6} + 5e^{5} + e^{4} - 26e^{3} + 11e^{2} + 26e - 8$
43 $[43, 43, -w^{2} + w - 1]$ $\phantom{-}2e^{5} - 3e^{4} - 12e^{3} + 11e^{2} + 19e - 10$
43 $[43, 43, w^{2} + w + 1]$ $-2e^{6} + 7e^{5} + 5e^{4} - 33e^{3} + 12e^{2} + 24e - 12$
49 $[49, 7, w^{3} + w^{2} - 6w - 3]$ $\phantom{-}3e^{6} - 10e^{5} - 11e^{4} + 50e^{3} - e^{2} - 47e + 12$
49 $[49, 7, w^{3} - w^{2} - 6w + 3]$ $-e^{6} + 3e^{5} + 3e^{4} - 11e^{3} + e^{2} + 3e + 2$
53 $[53, 53, 2w^{3} - w^{2} - 9w + 3]$ $\phantom{-}6e^{6} - 22e^{5} - 16e^{4} + 107e^{3} - 24e^{2} - 94e + 22$
53 $[53, 53, 2w^{3} + w^{2} - 9w - 3]$ $\phantom{-}2e^{6} - 5e^{5} - 12e^{4} + 28e^{3} + 19e^{2} - 32e - 6$
59 $[59, 59, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}e^{6} - 5e^{5} + 26e^{3} - 19e^{2} - 25e + 20$
59 $[59, 59, -w^{3} - w^{2} + 4w + 1]$ $\phantom{-}e^{5} + e^{4} - 8e^{3} - 7e^{2} + 10e + 6$
67 $[67, 67, 3w^{3} - 13w + 1]$ $\phantom{-}e^{6} - 5e^{5} - 2e^{4} + 25e^{3} - e^{2} - 24e - 4$
67 $[67, 67, -w^{3} + w^{2} + 6w - 5]$ $\phantom{-}2e^{6} - 8e^{5} - 2e^{4} + 37e^{3} - 23e^{2} - 33e + 16$
81 $[81, 3, -3]$ $\phantom{-}3e^{6} - 10e^{5} - 11e^{4} + 50e^{3} + e^{2} - 47e - 2$
83 $[83, 83, -2w^{3} - w^{2} + 9w + 7]$ $\phantom{-}e^{6} - e^{5} - 9e^{4} + 8e^{3} + 22e^{2} - 18e - 12$
83 $[83, 83, 4w^{3} - 18w - 1]$ $-3e^{6} + 10e^{5} + 10e^{4} - 49e^{3} - e^{2} + 49e + 6$
89 $[89, 89, -2w^{3} + 10w + 1]$ $\phantom{-}2e^{6} - 5e^{5} - 7e^{4} + 23e^{3} - 7e^{2} - 25e + 22$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
13 $[13,13,-w^{2}+w+3]$ $1$