Properties

Label 4.4.13448.1-5.1-c
Base field 4.4.13448.1
Weight $[2, 2, 2, 2]$
Level norm $5$
Level $[5, 5, -\frac{3}{2}w^{3} + \frac{1}{2}w^{2} + 10w - 4]$
Dimension $2$
CM no
Base change no

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Base field 4.4.13448.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[5, 5, -\frac{3}{2}w^{3} + \frac{1}{2}w^{2} + 10w - 4]$
Dimension: $2$
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:

\(x^{2} + x - 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}e$
4 $[4, 2, -w + 1]$ $\phantom{-}e - 1$
5 $[5, 5, -\frac{3}{2}w^{3} + \frac{1}{2}w^{2} + 10w - 4]$ $\phantom{-}1$
5 $[5, 5, \frac{3}{2}w^{3} + \frac{1}{2}w^{2} - 10w - 4]$ $-3$
25 $[25, 5, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 4]$ $-e - 1$
37 $[37, 37, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 4w]$ $-1$
37 $[37, 37, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 4w]$ $\phantom{-}5e + 2$
43 $[43, 43, -\frac{3}{2}w^{3} + \frac{1}{2}w^{2} + 10w - 2]$ $-4e - 1$
43 $[43, 43, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + 10w + 2]$ $-3e + 5$
49 $[49, 7, -w^{2} - w + 3]$ $\phantom{-}e + 8$
49 $[49, 7, -w^{2} + w + 3]$ $\phantom{-}2e - 4$
59 $[59, 59, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 2]$ $-6e - 3$
59 $[59, 59, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 2]$ $\phantom{-}7e + 3$
61 $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w + 2]$ $-4e - 10$
61 $[61, 61, \frac{3}{2}w^{3} + \frac{1}{2}w^{2} - 8w - 4]$ $-4e - 1$
73 $[73, 73, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + 2w]$ $\phantom{-}6e - 1$
73 $[73, 73, w^{2} - w + 1]$ $-4e - 4$
73 $[73, 73, w^{2} + w + 1]$ $-e - 13$
73 $[73, 73, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 2w]$ $-2e - 4$
81 $[81, 3, -3]$ $\phantom{-}2e - 5$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, -\frac{3}{2}w^{3} + \frac{1}{2}w^{2} + 10w - 4]$ $-1$