Properties

Label 4.4.4525.1-31.2-b
Base field 4.4.4525.1
Weight $[2, 2, 2, 2]$
Level norm $31$
Level $[31,31,\frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{5}{3}w + 5]$
Dimension $4$
CM no
Base change no

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Base field 4.4.4525.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[31,31,\frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{5}{3}w + 5]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $7$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{4} - 4x^{3} - 5x^{2} + 25x - 18\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -\frac{1}{3}w^{3} - \frac{2}{3}w^{2} + \frac{7}{3}w + 4]$ $\phantom{-}3e^{3} - 8e^{2} - 26e + 42$
5 $[5, 5, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{1}{3}w + 3]$ $\phantom{-}e$
9 $[9, 3, -w]$ $\phantom{-}2e^{3} - 5e^{2} - 18e + 26$
9 $[9, 3, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{7}{3}w + 1]$ $\phantom{-}2e^{3} - 5e^{2} - 18e + 26$
16 $[16, 2, 2]$ $-e - 1$
19 $[19, 19, \frac{2}{3}w^{3} - \frac{2}{3}w^{2} - \frac{11}{3}w]$ $-2e^{3} + 5e^{2} + 19e - 26$
19 $[19, 19, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{1}{3}w + 1]$ $\phantom{-}e^{3} - 2e^{2} - 9e + 10$
31 $[31, 31, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{11}{3}w - 2]$ $-3e^{3} + 7e^{2} + 26e - 32$
31 $[31, 31, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{5}{3}w + 5]$ $-1$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 6]$ $\phantom{-}6e^{3} - 15e^{2} - 52e + 78$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 3]$ $-7e^{3} + 19e^{2} + 61e - 96$
61 $[61, 61, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} + \frac{2}{3}w + 4]$ $\phantom{-}e^{3} - 2e^{2} - 10e + 10$
61 $[61, 61, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{14}{3}w - 2]$ $-6e^{3} + 16e^{2} + 49e - 80$
71 $[71, 71, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{1}{3}w - 7]$ $-e^{3} + 3e^{2} + 8e - 12$
71 $[71, 71, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - \frac{7}{3}w]$ $-e^{3} + e^{2} + 10e$
89 $[89, 89, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{10}{3}w - 3]$ $\phantom{-}2e^{3} - 6e^{2} - 18e + 30$
89 $[89, 89, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w - 1]$ $\phantom{-}12e^{3} - 33e^{2} - 103e + 168$
101 $[101, 101, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{7}{3}w - 3]$ $-12e^{3} + 33e^{2} + 102e - 162$
101 $[101, 101, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + \frac{11}{3}w - 4]$ $-4e^{3} + 10e^{2} + 37e - 48$
101 $[101, 101, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{8}{3}w + 3]$ $\phantom{-}13e^{3} - 35e^{2} - 110e + 174$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$31$ $[31,31,\frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{5}{3}w + 5]$ $1$