Properties

Base field 3.3.1101.1
Weight [2, 2, 2]
Level norm 12
Level $[12, 6, w^{2} + w - 5]$
Label 3.3.1101.1-12.2-c
Dimension 7
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 $[12, 6, w^{2} + w - 5]$
Label 3.3.1101.1-12.2-c
Dimension 7
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:
\(x^{7} \) \(\mathstrut -\mathstrut 2x^{6} \) \(\mathstrut -\mathstrut 11x^{5} \) \(\mathstrut +\mathstrut 20x^{4} \) \(\mathstrut +\mathstrut 32x^{3} \) \(\mathstrut -\mathstrut 45x^{2} \) \(\mathstrut -\mathstrut 32x \) \(\mathstrut +\mathstrut 21\)

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Norm Prime Eigenvalue
2 $[2, 2, w - 2]$ $\phantom{-}e$
3 $[3, 3, -w + 3]$ $\phantom{-}\frac{1}{2}e^{6} - \frac{1}{2}e^{5} - 5e^{4} + 4e^{3} + 10e^{2} - \frac{7}{2}e - \frac{3}{2}$
3 $[3, 3, w - 1]$ $\phantom{-}1$
4 $[4, 2, w^{2} + w - 7]$ $-1$
19 $[19, 19, w + 1]$ $\phantom{-}\frac{1}{2}e^{6} - \frac{1}{2}e^{5} - 5e^{4} + 3e^{3} + 9e^{2} + \frac{5}{2}e + \frac{5}{2}$
23 $[23, 23, w^{2} - 2w - 1]$ $-\frac{1}{2}e^{6} + \frac{1}{2}e^{5} + 4e^{4} - 3e^{3} - 3e^{2} - \frac{3}{2}e - \frac{9}{2}$
31 $[31, 31, -2w^{2} + 19]$ $-e^{5} + e^{4} + 10e^{3} - 8e^{2} - 17e + 7$
31 $[31, 31, -w^{2} + 5]$ $-e^{5} + 2e^{4} + 9e^{3} - 17e^{2} - 12e + 19$
31 $[31, 31, -3w + 5]$ $\phantom{-}\frac{1}{2}e^{6} + \frac{3}{2}e^{5} - 7e^{4} - 15e^{3} + 25e^{2} + \frac{61}{2}e - \frac{23}{2}$
41 $[41, 41, w^{2} + 2w - 7]$ $-e^{5} + 2e^{4} + 9e^{3} - 17e^{2} - 16e + 21$
43 $[43, 43, w^{2} - 11]$ $-e^{5} + 2e^{4} + 9e^{3} - 15e^{2} - 12e + 13$
47 $[47, 47, 3w - 7]$ $\phantom{-}\frac{1}{2}e^{6} + \frac{3}{2}e^{5} - 8e^{4} - 15e^{3} + 35e^{2} + \frac{55}{2}e - \frac{51}{2}$
53 $[53, 53, -3w^{2} - 6w + 11]$ $\phantom{-}e^{6} - e^{5} - 10e^{4} + 8e^{3} + 22e^{2} - 7e - 15$
59 $[59, 59, 2w - 1]$ $\phantom{-}e^{6} - 3e^{5} - 8e^{4} + 26e^{3} + 4e^{2} - 33e + 9$
67 $[67, 67, 2w^{2} + w - 19]$ $-\frac{1}{2}e^{6} + \frac{5}{2}e^{5} + e^{4} - 23e^{3} + 21e^{2} + \frac{75}{2}e - \frac{53}{2}$
67 $[67, 67, 3w^{2} + 2w - 25]$ $\phantom{-}e^{5} - e^{4} - 8e^{3} + 8e^{2} + 7e - 11$
67 $[67, 67, w - 5]$ $-2e^{6} + e^{5} + 21e^{4} - 4e^{3} - 50e^{2} - 13e + 19$
73 $[73, 73, -4w^{2} - 3w + 29]$ $\phantom{-}\frac{3}{2}e^{6} - \frac{1}{2}e^{5} - 17e^{4} + 2e^{3} + 48e^{2} + \frac{7}{2}e - \frac{55}{2}$
73 $[73, 73, 2w^{2} - w - 11]$ $-e^{6} - e^{5} + 12e^{4} + 10e^{3} - 34e^{2} - 19e + 7$
73 $[73, 73, w^{2} + 2w - 11]$ $-2e^{6} + 2e^{5} + 20e^{4} - 16e^{3} - 42e^{2} + 14e + 14$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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