Properties

Base field 4.4.13888.1
Weight [2, 2, 2, 2]
Level norm 7
Level $[7, 7, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - \frac{7}{3}w + 1]$
Label 4.4.13888.1-7.1-d
Dimension 3
CM no
Base change no

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Base field 4.4.13888.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 6x + 9\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[7, 7, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - \frac{7}{3}w + 1]$
Label 4.4.13888.1-7.1-d
Dimension 3
Is CM no
Is base change no
Parent newspace dimension 8

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} \) \(\mathstrut +\mathstrut 2x^{2} \) \(\mathstrut -\mathstrut 6x \) \(\mathstrut -\mathstrut 11\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{4}{3}w - 1]$ $\phantom{-}e$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - \frac{7}{3}w + 1]$ $\phantom{-}1$
7 $[7, 7, w - 2]$ $\phantom{-}e^{2} - 7$
7 $[7, 7, w - 1]$ $\phantom{-}e^{2} - e - 8$
9 $[9, 3, w]$ $\phantom{-}e^{2} + e - 6$
9 $[9, 3, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{7}{3}w - 2]$ $-2e^{2} - e + 9$
23 $[23, 23, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{1}{3}w - 2]$ $-e^{2} + e + 6$
23 $[23, 23, -\frac{2}{3}w^{3} + \frac{4}{3}w^{2} + \frac{11}{3}w - 4]$ $\phantom{-}2e^{2} - e - 11$
31 $[31, 31, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + \frac{14}{3}w + 2]$ $-2e^{2} - e + 5$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{4}{3}w - 7]$ $\phantom{-}2e^{2} - 4$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{4}{3}w - 4]$ $-3e^{2} - e + 12$
47 $[47, 47, \frac{1}{3}w^{3} - \frac{5}{3}w^{2} - \frac{1}{3}w + 5]$ $-4e^{2} + 20$
47 $[47, 47, w^{2} - w - 4]$ $\phantom{-}2e^{2} - 12$
73 $[73, 73, -w^{3} + 3w^{2} + 4w - 8]$ $\phantom{-}3e + 1$
73 $[73, 73, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} - \frac{1}{3}w - 4]$ $-2e^{2} - 3e + 5$
73 $[73, 73, -w^{3} + w^{2} + 7w + 1]$ $\phantom{-}6$
73 $[73, 73, \frac{2}{3}w^{3} - \frac{4}{3}w^{2} - \frac{14}{3}w + 5]$ $\phantom{-}3e^{2} + 5e - 14$
79 $[79, 79, w^{2} - 5]$ $-e^{2} + 3e + 4$
79 $[79, 79, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} + \frac{8}{3}w - 6]$ $\phantom{-}e^{2} + 2e + 3$
97 $[97, 97, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} + \frac{5}{3}w - 4]$ $-e^{2} - 4e + 7$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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