Properties

Base field 4.4.18688.1
Weight [2, 2, 2, 2]
Level norm 7
Level $[7, 7, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{7}{3}]$
Label 4.4.18688.1-7.1-a
Dimension 5
CM no
Base change no

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Base field 4.4.18688.1

Generator \(w\), with minimal polynomial \(x^{4} - 10x^{2} - 4x + 14\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[7, 7, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{7}{3}]$
Label 4.4.18688.1-7.1-a
Dimension 5
Is CM no
Is base change no
Parent newspace dimension 10

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} \) \(\mathstrut -\mathstrut 3x^{4} \) \(\mathstrut -\mathstrut x^{3} \) \(\mathstrut +\mathstrut 7x^{2} \) \(\mathstrut -\mathstrut 2x \) \(\mathstrut -\mathstrut 1\)

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Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $\phantom{-}e$
7 $[7, 7, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{7}{3}]$ $-1$
7 $[7, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + w - \frac{5}{3}]$ $-e^{4} + 2e^{3} + 3e^{2} - 4e$
9 $[9, 3, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{5}{3}]$ $\phantom{-}2e^{3} - 2e^{2} - 5e + 1$
9 $[9, 3, w + 1]$ $\phantom{-}e^{4} - 3e^{3} - e^{2} + 7e - 2$
17 $[17, 17, w + 3]$ $\phantom{-}e^{4} - 3e^{3} + 6e - 3$
17 $[17, 17, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{11}{3}]$ $-2e^{4} + 3e^{3} + 7e^{2} - 8e - 3$
31 $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - w - \frac{1}{3}]$ $\phantom{-}3e^{4} - 10e^{3} - e^{2} + 19e - 4$
31 $[31, 31, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{1}{3}]$ $-2e^{4} + 7e^{3} + 4e^{2} - 18e - 1$
41 $[41, 41, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 4w - \frac{19}{3}]$ $\phantom{-}2e^{4} - e^{3} - 8e^{2} - e + 4$
41 $[41, 41, w^{2} - 5]$ $-5e^{4} + 10e^{3} + 12e^{2} - 16e - 4$
41 $[41, 41, 2w + 3]$ $-3e^{4} + 6e^{3} + 4e^{2} - 9e + 7$
41 $[41, 41, \frac{2}{3}w^{3} + \frac{4}{3}w^{2} - 5w - \frac{29}{3}]$ $-3e^{4} + 4e^{3} + 13e^{2} - 11e - 8$
47 $[47, 47, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 3w - \frac{19}{3}]$ $\phantom{-}3e^{4} - e^{3} - 13e^{2} - 2e + 8$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - \frac{13}{3}]$ $-2e^{3} + e^{2} + 8e$
49 $[49, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - \frac{11}{3}]$ $-3e^{4} + 6e^{3} + 6e^{2} - 10e - 4$
73 $[73, 73, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 5w + \frac{19}{3}]$ $\phantom{-}6e^{4} - 9e^{3} - 19e^{2} + 19e + 5$
73 $[73, 73, -\frac{2}{3}w^{3} - \frac{1}{3}w^{2} + 4w + \frac{11}{3}]$ $\phantom{-}6e^{4} - 17e^{3} - 9e^{2} + 32e + 2$
73 $[73, 73, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + 2w - \frac{17}{3}]$ $-e^{4} + 2e^{3} + 2e^{2} - 3e + 1$
103 $[103, 103, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + w - \frac{23}{3}]$ $-3e^{4} + 6e^{3} + 8e^{2} - 10e + 9$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{7}{3}]$ $1$