Properties

Label 4.4.13968.1-13.1-c
Base field 4.4.13968.1
Weight $[2, 2, 2, 2]$
Level norm $13$
Level $[13, 13, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 2]$
Dimension $2$
CM no
Base change no

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Base field 4.4.13968.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 8x + 4\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[13, 13, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 2]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $30$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 5\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, \frac{1}{2}w^{2} + \frac{1}{2}w - 1]$ $\phantom{-}1$
2 $[2, 2, -\frac{1}{2}w^{2} + \frac{3}{2}w]$ $\phantom{-}e$
9 $[9, 3, -\frac{1}{2}w^{2} + \frac{1}{2}w + 2]$ $-2$
13 $[13, 13, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 2]$ $\phantom{-}1$
13 $[13, 13, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 1]$ $-e - 3$
23 $[23, 23, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w]$ $-2e - 2$
23 $[23, 23, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 3]$ $-e + 7$
37 $[37, 37, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w - 3]$ $\phantom{-}2e$
37 $[37, 37, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 6]$ $-e + 5$
59 $[59, 59, -\frac{1}{2}w^{3} + \frac{7}{2}w]$ $\phantom{-}2e - 10$
59 $[59, 59, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 2w - 3]$ $\phantom{-}4e + 4$
61 $[61, 61, -w^{3} + 2w^{2} + 7w - 7]$ $-2e - 4$
61 $[61, 61, w^{3} - w^{2} - 6w + 3]$ $-2e - 8$
61 $[61, 61, w^{3} - 2w^{2} - 5w + 3]$ $\phantom{-}4e + 2$
61 $[61, 61, w^{3} - w^{2} - 8w + 1]$ $-2e$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 5]$ $-e - 9$
71 $[71, 71, -w^{3} + \frac{3}{2}w^{2} + \frac{15}{2}w - 6]$ $-3e - 3$
83 $[83, 83, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 2w - 7]$ $-4e + 4$
83 $[83, 83, \frac{1}{2}w^{3} - \frac{7}{2}w - 4]$ $\phantom{-}e + 1$
97 $[97, 97, 2w - 1]$ $-6e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 2]$ $-1$