Properties

Label 3.3.1076.1-13.2-c
Base field 3.3.1076.1
Weight $[2, 2, 2]$
Level norm $13$
Level $[13, 13, 2w + 5]$
Dimension $4$
CM no
Base change no

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Base field 3.3.1076.1

Generator \(w\), with minimal polynomial \(x^{3} - 8x - 6\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[13, 13, 2w + 5]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $22$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 5x^{2} + 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $-1$
3 $[3, 3, -w^{2} + 2w + 3]$ $\phantom{-}e$
7 $[7, 7, -2w^{2} + 5w + 5]$ $-e^{3} + 5e$
9 $[9, 3, -w^{2} + 5]$ $\phantom{-}e^{3} - 5e$
13 $[13, 13, -w^{2} + 3w + 1]$ $-3e^{3} + 12e$
13 $[13, 13, 2w + 5]$ $-1$
13 $[13, 13, w - 1]$ $\phantom{-}e^{3} - 7e$
17 $[17, 17, w^{2} - w - 5]$ $\phantom{-}e^{3} - 3e$
19 $[19, 19, w^{2} - 2w - 5]$ $\phantom{-}3e^{2} - 10$
29 $[29, 29, w^{2} - 7]$ $-e^{3} + 3e$
31 $[31, 31, 2w^{2} - 3w - 11]$ $-4e^{2} + 10$
49 $[49, 7, -2w^{2} - 4w + 1]$ $\phantom{-}5e^{3} - 20e$
59 $[59, 59, w^{2} - 2w - 11]$ $-2e^{2} + 6$
71 $[71, 71, -2w + 7]$ $\phantom{-}e^{2} - 14$
73 $[73, 73, w^{2} - 3w - 13]$ $-e^{2} + 2$
73 $[73, 73, 2w^{2} - 2w - 17]$ $\phantom{-}4e^{2} - 6$
73 $[73, 73, -w^{2} - 4w - 5]$ $-3e^{2} + 6$
79 $[79, 79, 2w - 1]$ $-4e^{3} + 16e$
79 $[79, 79, w^{2} + w - 5]$ $\phantom{-}3e$
79 $[79, 79, w - 5]$ $-3e^{2} + 10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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