Properties

Base field 4.4.16997.1
Weight [2, 2, 2, 2]
Level norm 13
Level $[13, 13, w^{2} - w - 4]$
Label 4.4.16997.1-13.2-a
Dimension 12
CM no
Base change no

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Base field 4.4.16997.1

Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[13, 13, w^{2} - w - 4]$
Label 4.4.16997.1-13.2-a
Dimension 12
Is CM no
Is base change no
Parent newspace dimension 26

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{12} + 6x^{11} - 17x^{10} - 125x^{9} + 122x^{8} + 924x^{7} - 611x^{6} - 2701x^{5} + 1871x^{4} + 2290x^{3} - 1645x^{2} - 369x + 245\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w]$ $...$
5 $[5, 5, -w^{2} + w + 2]$ $\phantom{-}e$
7 $[7, 7, -w^{2} + 2]$ $...$
13 $[13, 13, -w^{2} + 3]$ $...$
13 $[13, 13, w^{2} - w - 4]$ $\phantom{-}1$
16 $[16, 2, 2]$ $...$
19 $[19, 19, -w^{2} + w + 1]$ $...$
23 $[23, 23, -w^{3} + 4w + 2]$ $...$
25 $[25, 5, -w^{3} + w^{2} + 3w - 1]$ $...$
29 $[29, 29, w^{3} - w^{2} - 4w + 1]$ $...$
29 $[29, 29, -w + 3]$ $...$
31 $[31, 31, -w^{3} + w^{2} + 5w - 2]$ $...$
37 $[37, 37, w^{3} - 4w - 1]$ $...$
37 $[37, 37, w^{3} - 3w + 1]$ $...$
53 $[53, 53, -w^{3} + 2w^{2} + 4w - 6]$ $...$
59 $[59, 59, w^{2} + w - 4]$ $...$
61 $[61, 61, -2w^{2} + w + 8]$ $...$
73 $[73, 73, -w^{3} + 5w - 1]$ $...$
79 $[79, 79, 2w^{2} + w - 6]$ $...$
79 $[79, 79, 2w^{3} - w^{2} - 9w + 3]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
13 $[13, 13, w^{2} - w - 4]$ $-1$