Properties

Label 4.4.19525.1-5.1-a
Base field 4.4.19525.1
Weight $[2, 2, 2, 2]$
Level norm $5$
Level $[5, 5, \frac{2}{3}w^{2} + \frac{1}{3}w - 5]$
Dimension $4$
CM no
Base change no

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Base field 4.4.19525.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 14x^{2} + 15x + 45\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[5, 5, \frac{2}{3}w^{2} + \frac{1}{3}w - 5]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 6x^{3} + 8x^{2} + 4x - 6\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, \frac{2}{3}w^{2} + \frac{1}{3}w - 5]$ $-1$
5 $[5, 5, \frac{2}{3}w^{2} - \frac{5}{3}w - 4]$ $\phantom{-}e$
9 $[9, 3, -w + 3]$ $-e^{3} + 5e^{2} - 4e - 4$
9 $[9, 3, w + 2]$ $\phantom{-}2e^{3} - 8e^{2} + 2e + 8$
11 $[11, 11, \frac{2}{3}w^{2} + \frac{1}{3}w - 4]$ $\phantom{-}e^{2} - 3e$
16 $[16, 2, 2]$ $-e^{2} + 3e - 1$
19 $[19, 19, \frac{1}{3}w^{3} - \frac{10}{3}w - 3]$ $\phantom{-}2e^{3} - 8e^{2} + 2e + 6$
19 $[19, 19, \frac{1}{3}w^{3} - w^{2} - \frac{7}{3}w + 6]$ $-e^{3} + 5e^{2} - 3e$
29 $[29, 29, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 2]$ $-2e^{2} + 3e + 6$
29 $[29, 29, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $\phantom{-}2e^{3} - 7e^{2} - 3e + 12$
31 $[31, 31, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w + 1]$ $\phantom{-}2e^{3} - 7e^{2} - e + 6$
31 $[31, 31, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 4]$ $-2e^{2} + 6e + 6$
49 $[49, 7, \frac{1}{3}w^{3} - \frac{10}{3}w - 1]$ $-e^{3} + 4e^{2} + 4e - 6$
49 $[49, 7, -\frac{1}{3}w^{3} + w^{2} + \frac{7}{3}w - 4]$ $-e^{3} + 3e^{2} - e$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{5}{3}w - 11]$ $-e^{3} + 3e^{2} + 2e - 6$
59 $[59, 59, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 5w - 13]$ $\phantom{-}2e^{3} - 10e^{2} + 8e + 6$
61 $[61, 61, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{2}{3}w - 9]$ $-e^{3} + e^{2} + 4e + 4$
61 $[61, 61, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 4w + 2]$ $-e^{3} + 2e^{2} + 4e + 6$
61 $[61, 61, \frac{2}{3}w^{2} - \frac{5}{3}w - 1]$ $-e^{3} + 2e^{2} + 3e$
61 $[61, 61, -\frac{1}{3}w^{2} + \frac{4}{3}w + 6]$ $\phantom{-}e^{3} - 3e^{2} + 2e - 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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