Properties

Label 3.3.1937.1-13.2-a
Base field 3.3.1937.1
Weight $[2, 2, 2]$
Level norm $13$
Level $[13, 13, -w + 2]$
Dimension $2$
CM no
Base change no

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Base field 3.3.1937.1

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

Form

Weight: $[2, 2, 2]$
Level: $[13, 13, -w + 2]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $44$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w - 2]$ $\phantom{-}e$
5 $[5, 5, w + 1]$ $\phantom{-}e$
7 $[7, 7, w - 3]$ $\phantom{-}4$
8 $[8, 2, 2]$ $-3$
9 $[9, 3, w^{2} - 3w - 2]$ $\phantom{-}3e$
13 $[13, 13, w + 3]$ $-2$
13 $[13, 13, -w + 2]$ $\phantom{-}1$
19 $[19, 19, -w^{2} + 2w + 4]$ $\phantom{-}4e$
23 $[23, 23, w^{2} - 4w + 1]$ $\phantom{-}0$
25 $[25, 5, w^{2} - 2w - 1]$ $-4e$
31 $[31, 31, w^{2} - 2w - 9]$ $-4e$
37 $[37, 37, -w^{2} + 3w + 3]$ $\phantom{-}e$
41 $[41, 41, w^{2} - w - 1]$ $-7e$
41 $[41, 41, w^{2} - w - 5]$ $\phantom{-}7e$
41 $[41, 41, w^{2} - w - 10]$ $\phantom{-}2$
43 $[43, 43, -2w - 3]$ $-2e$
47 $[47, 47, -w^{2} - w + 4]$ $-4$
49 $[49, 7, -w^{2} + 5w - 5]$ $\phantom{-}12$
59 $[59, 59, w^{2} - w - 4]$ $\phantom{-}0$
59 $[59, 59, w^{2} - 3]$ $\phantom{-}7e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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