Properties

Base field 3.3.1101.1
Weight [2, 2, 2]
Level norm 12
Level $[12, 6, w^{2} + w - 9]$
Label 3.3.1101.1-12.1-e
Dimension 5
CM no
Base change no

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Base field 3.3.1101.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 12\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2]
Level $[12, 6, w^{2} + w - 9]$
Label 3.3.1101.1-12.1-e
Dimension 5
Is CM no
Is base change no
Parent newspace dimension 13

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} \) \(\mathstrut -\mathstrut x^{4} \) \(\mathstrut -\mathstrut 8x^{3} \) \(\mathstrut +\mathstrut 6x^{2} \) \(\mathstrut +\mathstrut 13x \) \(\mathstrut -\mathstrut 3\)

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Norm Prime Eigenvalue
2 $[2, 2, w - 2]$ $\phantom{-}e$
3 $[3, 3, -w + 3]$ $-1$
3 $[3, 3, w - 1]$ $\phantom{-}\frac{1}{2}e^{4} - 3e^{2} + \frac{5}{2}$
4 $[4, 2, w^{2} + w - 7]$ $\phantom{-}1$
19 $[19, 19, w + 1]$ $-e^{2} + 5$
23 $[23, 23, w^{2} - 2w - 1]$ $\phantom{-}e^{3} - 2e^{2} - 5e + 6$
31 $[31, 31, -2w^{2} + 19]$ $-\frac{3}{2}e^{4} + 9e^{2} - e - \frac{5}{2}$
31 $[31, 31, -w^{2} + 5]$ $-\frac{1}{2}e^{4} + e^{3} + 3e^{2} - 5e - \frac{5}{2}$
31 $[31, 31, -3w + 5]$ $\phantom{-}\frac{1}{2}e^{4} - 2e^{3} - 4e^{2} + 11e + \frac{13}{2}$
41 $[41, 41, w^{2} + 2w - 7]$ $-e^{3} + 3e$
43 $[43, 43, w^{2} - 11]$ $-\frac{1}{2}e^{4} - e^{3} + 2e^{2} + 4e + \frac{7}{2}$
47 $[47, 47, 3w - 7]$ $-\frac{1}{2}e^{4} + e^{3} - 4e + \frac{15}{2}$
53 $[53, 53, -3w^{2} - 6w + 11]$ $\phantom{-}\frac{1}{2}e^{4} + 2e^{3} - 2e^{2} - 10e - \frac{9}{2}$
59 $[59, 59, 2w - 1]$ $\phantom{-}\frac{3}{2}e^{4} - e^{3} - 8e^{2} + 3e + \frac{9}{2}$
67 $[67, 67, 2w^{2} + w - 19]$ $-e^{4} - e^{3} + 8e^{2} + 7e - 13$
67 $[67, 67, 3w^{2} + 2w - 25]$ $-e^{4} + e^{3} + 8e^{2} - 9e - 7$
67 $[67, 67, w - 5]$ $\phantom{-}\frac{1}{2}e^{4} - 2e^{2} + 4e - \frac{5}{2}$
73 $[73, 73, -4w^{2} - 3w + 29]$ $-e^{4} - 2e^{3} + 7e^{2} + 10e - 4$
73 $[73, 73, 2w^{2} - w - 11]$ $\phantom{-}\frac{3}{2}e^{4} - 3e^{3} - 11e^{2} + 14e + \frac{25}{2}$
73 $[73, 73, w^{2} + 2w - 11]$ $\phantom{-}2e^{3} + 2e^{2} - 14e - 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w + 3]$ $1$
4 $[4, 2, w^{2} + w - 7]$ $-1$