Properties

Base field 3.3.733.1
Weight [2, 2, 2]
Level norm 13
Level $[13, 13, w + 1]$
Label 3.3.733.1-13.1-d
Dimension 6
CM no
Base change no

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Base field 3.3.733.1

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

Form

Weight [2, 2, 2]
Level $[13, 13, w + 1]$
Label 3.3.733.1-13.1-d
Dimension 6
Is CM no
Is base change no
Parent newspace dimension 11

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} \) \(\mathstrut -\mathstrut x^{5} \) \(\mathstrut -\mathstrut 8x^{4} \) \(\mathstrut +\mathstrut 5x^{3} \) \(\mathstrut +\mathstrut 18x^{2} \) \(\mathstrut -\mathstrut 4x \) \(\mathstrut -\mathstrut 7\)

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Norm Prime Eigenvalue
2 $[2, 2, -w + 2]$ $\phantom{-}e$
4 $[4, 2, -w^{2} - w + 5]$ $\phantom{-}e^{4} - e^{3} - 4e^{2} + 3e + 2$
5 $[5, 5, -w + 3]$ $-e^{4} + e^{3} + 5e^{2} - 3e - 4$
7 $[7, 7, -w^{2} - 2w + 3]$ $-e^{4} + 6e^{2} - 5$
11 $[11, 11, -w^{2} + 5]$ $-e^{4} - 2e^{3} + 6e^{2} + 8e - 3$
13 $[13, 13, w + 1]$ $\phantom{-}1$
23 $[23, 23, w^{2} - 3]$ $\phantom{-}e^{5} - e^{4} - 6e^{3} + 4e^{2} + 9e + 1$
25 $[25, 5, w^{2} + 2w - 1]$ $\phantom{-}e^{4} - e^{3} - 2e^{2} + e - 5$
27 $[27, 3, -3]$ $\phantom{-}e^{5} - e^{4} - 5e^{3} + 3e^{2} + 6e$
29 $[29, 29, -3w + 7]$ $\phantom{-}e^{5} - 7e^{3} - e^{2} + 10e - 1$
43 $[43, 43, -3w^{2} - 2w + 17]$ $-e^{5} + e^{4} + 5e^{3} - 3e^{2} - 4e + 2$
49 $[49, 7, -2w^{2} + w + 11]$ $\phantom{-}2e^{2} - 8$
67 $[67, 67, -2w^{2} - 4w + 3]$ $-e^{4} - e^{3} + 4e^{2} + 3e + 3$
71 $[71, 71, -2w^{2} + w + 9]$ $-e^{5} + e^{4} + 5e^{3} - 4e - 9$
73 $[73, 73, w^{2} + 2w - 7]$ $-e^{5} + 10e^{3} - 2e^{2} - 27e + 2$
73 $[73, 73, -2w^{2} - 2w + 11]$ $\phantom{-}e^{5} - 4e^{4} - 4e^{3} + 14e^{2} + 7e + 4$
73 $[73, 73, w - 5]$ $\phantom{-}3e^{5} - e^{4} - 13e^{3} - 4e^{2} + 4e + 17$
89 $[89, 89, 2w^{2} + w - 9]$ $-2e^{5} + 2e^{4} + 14e^{3} - 8e^{2} - 20e$
89 $[89, 89, -w^{2} - 2w + 9]$ $\phantom{-}e^{5} + e^{4} - 6e^{3} - 10e^{2} + 5e + 19$
89 $[89, 89, -2w - 1]$ $\phantom{-}2e^{5} + 2e^{4} - 17e^{3} - 9e^{2} + 31e + 5$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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