Properties

Label 3.3.1257.1-13.2-a
Base field 3.3.1257.1
Weight $[2, 2, 2]$
Level norm $13$
Level $[13, 13, -2w + 5]$
Dimension $2$
CM no
Base change no

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Base field 3.3.1257.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x + 9\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[13, 13, -2w + 5]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $24$

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
3 $[3, 3, -w + 3]$ $\phantom{-}e$
3 $[3, 3, w - 2]$ $\phantom{-}1$
5 $[5, 5, w^{2} + w - 5]$ $\phantom{-}e + 2$
8 $[8, 2, 2]$ $\phantom{-}e - 4$
13 $[13, 13, w + 2]$ $\phantom{-}e + 1$
13 $[13, 13, -2w + 5]$ $\phantom{-}1$
13 $[13, 13, -w^{2} - w + 4]$ $\phantom{-}2e - 3$
19 $[19, 19, -w^{2} + w + 4]$ $\phantom{-}e - 2$
23 $[23, 23, -w^{2} - w + 7]$ $-3$
25 $[25, 5, w^{2} - 2w - 1]$ $\phantom{-}e + 4$
29 $[29, 29, w^{2} - 5]$ $-3e + 6$
31 $[31, 31, w^{2} + w - 8]$ $-4$
41 $[41, 41, w^{2} + w - 11]$ $\phantom{-}2e + 7$
47 $[47, 47, w^{2} + 2w - 1]$ $\phantom{-}2e - 5$
59 $[59, 59, w^{2} + w - 1]$ $-12$
61 $[61, 61, -w^{2} + 5w - 7]$ $-5e + 1$
67 $[67, 67, 2w^{2} - 13]$ $-2e - 5$
89 $[89, 89, -2w^{2} + w + 20]$ $-2e - 1$
89 $[89, 89, 5w^{2} + 8w - 19]$ $\phantom{-}8e - 5$
89 $[89, 89, w^{2} + 2w - 7]$ $-2e - 10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, -2w + 5]$ $-1$