Properties

Base field 4.4.13888.1
Weight [2, 2, 2, 2]
Level norm 23
Level $[23,23,-\frac{2}{3}w^{3} + \frac{4}{3}w^{2} + \frac{11}{3}w - 4]$
Label 4.4.13888.1-23.2-d
Dimension 4
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 $[23,23,-\frac{2}{3}w^{3} + \frac{4}{3}w^{2} + \frac{11}{3}w - 4]$
Label 4.4.13888.1-23.2-d
Dimension 4
Is CM no
Is base change no
Parent newspace dimension 28

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} \) \(\mathstrut -\mathstrut 6x^{3} \) \(\mathstrut -\mathstrut 3x^{2} \) \(\mathstrut +\mathstrut 36x \) \(\mathstrut -\mathstrut 27\)

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Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{4}{3}w - 1]$ $\phantom{-}\frac{2}{9}e^{3} - e^{2} - \frac{8}{3}e + 4$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - \frac{7}{3}w + 1]$ $\phantom{-}\frac{2}{9}e^{3} - e^{2} - \frac{5}{3}e + 4$
7 $[7, 7, w - 2]$ $-\frac{1}{3}e^{3} + \frac{4}{3}e^{2} + 3e - 5$
7 $[7, 7, w - 1]$ $-\frac{2}{9}e^{3} + e^{2} + \frac{5}{3}e - 4$
9 $[9, 3, w]$ $\phantom{-}\frac{1}{9}e^{3} - \frac{2}{3}e^{2} - \frac{1}{3}e + 3$
9 $[9, 3, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{7}{3}w - 2]$ $\phantom{-}\frac{1}{3}e^{2} - e - 2$
23 $[23, 23, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{1}{3}w - 2]$ $-\frac{2}{9}e^{3} + e^{2} + \frac{8}{3}e - 1$
23 $[23, 23, -\frac{2}{3}w^{3} + \frac{4}{3}w^{2} + \frac{11}{3}w - 4]$ $\phantom{-}1$
31 $[31, 31, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + \frac{14}{3}w + 2]$ $-5$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{4}{3}w - 7]$ $-\frac{1}{3}e^{3} + 2e^{2} + e - 9$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{4}{3}w - 4]$ $\phantom{-}\frac{4}{9}e^{3} - 2e^{2} - \frac{10}{3}e + 8$
47 $[47, 47, \frac{1}{3}w^{3} - \frac{5}{3}w^{2} - \frac{1}{3}w + 5]$ $\phantom{-}\frac{7}{9}e^{3} - 3e^{2} - \frac{22}{3}e + 11$
47 $[47, 47, w^{2} - w - 4]$ $\phantom{-}\frac{4}{3}e^{3} - 6e^{2} - 10e + 24$
73 $[73, 73, -w^{3} + 3w^{2} + 4w - 8]$ $\phantom{-}\frac{2}{9}e^{3} - \frac{14}{3}e - 2$
73 $[73, 73, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} - \frac{1}{3}w - 4]$ $\phantom{-}\frac{4}{9}e^{3} - 2e^{2} - \frac{16}{3}e + 8$
73 $[73, 73, -w^{3} + w^{2} + 7w + 1]$ $-\frac{10}{9}e^{3} + 5e^{2} + \frac{40}{3}e - 26$
73 $[73, 73, \frac{2}{3}w^{3} - \frac{4}{3}w^{2} - \frac{14}{3}w + 5]$ $\phantom{-}\frac{2}{9}e^{3} - 2e^{2} + \frac{4}{3}e + 10$
79 $[79, 79, w^{2} - 5]$ $-\frac{1}{3}e^{3} + \frac{2}{3}e^{2} + 5e - 1$
79 $[79, 79, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} + \frac{8}{3}w - 6]$ $\phantom{-}e^{3} - \frac{16}{3}e^{2} - 5e + 23$
97 $[97, 97, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} + \frac{5}{3}w - 4]$ $-\frac{2}{3}e^{3} + \frac{7}{3}e^{2} + 7e - 8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
23 $[23,23,-\frac{2}{3}w^{3} + \frac{4}{3}w^{2} + \frac{11}{3}w - 4]$ $-1$