Properties

Base field 3.3.1101.1
Weight [2, 2, 2]
Level norm 3
Level $[3, 3, -w + 3]$
Label 3.3.1101.1-3.1-a
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 $[3, 3, -w + 3]$
Label 3.3.1101.1-3.1-a
Dimension 5
Is CM no
Is base change no
Parent newspace dimension 5

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} \) \(\mathstrut -\mathstrut 2x^{4} \) \(\mathstrut -\mathstrut 6x^{3} \) \(\mathstrut +\mathstrut 10x^{2} \) \(\mathstrut +\mathstrut 8x \) \(\mathstrut -\mathstrut 7\)

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Norm Prime Eigenvalue
2 $[2, 2, w - 2]$ $\phantom{-}e$
3 $[3, 3, -w + 3]$ $\phantom{-}1$
3 $[3, 3, w - 1]$ $\phantom{-}e^{4} - 6e^{2} - e + 6$
4 $[4, 2, w^{2} + w - 7]$ $-e^{4} + e^{3} + 5e^{2} - 3e - 3$
19 $[19, 19, w + 1]$ $-2e^{4} - 2e^{3} + 12e^{2} + 10e - 6$
23 $[23, 23, w^{2} - 2w - 1]$ $-e^{3} + 3e^{2} + 2e - 8$
31 $[31, 31, -2w^{2} + 19]$ $-4e^{2} + 2e + 10$
31 $[31, 31, -w^{2} + 5]$ $-2e^{4} + 10e^{2}$
31 $[31, 31, -3w + 5]$ $\phantom{-}2e^{4} - e^{3} - 9e^{2} + 4$
41 $[41, 41, w^{2} + 2w - 7]$ $-2e^{4} + 12e^{2} + 2e - 14$
43 $[43, 43, w^{2} - 11]$ $\phantom{-}4e^{3} - 2e^{2} - 16e + 2$
47 $[47, 47, 3w - 7]$ $\phantom{-}2e^{4} + 2e^{3} - 10e^{2} - 8e - 2$
53 $[53, 53, -3w^{2} - 6w + 11]$ $\phantom{-}2e^{4} - 12e^{2} - 4e + 12$
59 $[59, 59, 2w - 1]$ $\phantom{-}3e^{3} - 3e^{2} - 10e + 10$
67 $[67, 67, 2w^{2} + w - 19]$ $-e^{4} + 2e^{3} + 4e^{2} - 7e + 2$
67 $[67, 67, 3w^{2} + 2w - 25]$ $\phantom{-}2e^{2} + 2e - 8$
67 $[67, 67, w - 5]$ $\phantom{-}2e^{4} - 12e^{2} + 14$
73 $[73, 73, -4w^{2} - 3w + 29]$ $\phantom{-}4e^{4} - 2e^{3} - 18e^{2} + 4e + 6$
73 $[73, 73, 2w^{2} - w - 11]$ $\phantom{-}6e^{4} - 2e^{3} - 32e^{2} + 4e + 22$
73 $[73, 73, w^{2} + 2w - 11]$ $-4e^{4} - 3e^{3} + 23e^{2} + 18e - 16$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w + 3]$ $-1$