Properties

Base field 3.3.316.1
Weight [2, 2, 2]
Level norm 11
Level $[11, 11, w^{2} - w - 1]$
Label 3.3.316.1-11.1-a
Dimension 5
CM no
Base change no

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Base field 3.3.316.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 4x + 2\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2]
Level $[11, 11, w^{2} - w - 1]$
Label 3.3.316.1-11.1-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:
\(x^{5} \) \(\mathstrut -\mathstrut x^{4} \) \(\mathstrut -\mathstrut 10x^{3} \) \(\mathstrut +\mathstrut 8x^{2} \) \(\mathstrut +\mathstrut 20x \) \(\mathstrut -\mathstrut 4\)

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Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}e$
2 $[2, 2, w - 1]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + 3e + 2$
11 $[11, 11, w^{2} - w - 1]$ $\phantom{-}1$
17 $[17, 17, -w^{2} - w + 3]$ $-e^{4} + 7e^{2} - 4$
19 $[19, 19, w^{2} - w + 1]$ $\phantom{-}e^{2} - e - 6$
23 $[23, 23, 2w - 3]$ $-e^{4} - e^{3} + 6e^{2} + 6e$
27 $[27, 3, 3]$ $\phantom{-}e^{3} + e^{2} - 8e - 4$
29 $[29, 29, 2w + 1]$ $-e^{3} + 5e + 2$
31 $[31, 31, 2w^{2} - 2w - 9]$ $\phantom{-}e^{4} + e^{3} - 7e^{2} - 5e + 2$
37 $[37, 37, 2w^{2} - 2w - 5]$ $-e^{4} + 8e^{2} - e - 10$
41 $[41, 41, 2w^{2} - 9]$ $\phantom{-}e^{4} + 2e^{3} - 7e^{2} - 12e + 6$
43 $[43, 43, w^{2} + w - 5]$ $\phantom{-}2e^{2} - 2e - 8$
43 $[43, 43, -3w^{2} + w + 15]$ $\phantom{-}e^{4} - e^{3} - 9e^{2} + 7e + 10$
43 $[43, 43, -2w^{2} + 2w + 11]$ $-e^{3} - e^{2} + 4e + 8$
53 $[53, 53, w^{2} - w - 7]$ $\phantom{-}e^{4} + 2e^{3} - 8e^{2} - 13e + 10$
61 $[61, 61, 4w^{2} - 2w - 15]$ $-e^{4} + 9e^{2} - 2e - 12$
67 $[67, 67, -5w^{2} + 3w + 23]$ $\phantom{-}2e^{3} - e^{2} - 13e + 2$
73 $[73, 73, 2w^{2} - 3]$ $-e^{4} - 2e^{3} + 7e^{2} + 10e - 4$
73 $[73, 73, -3w^{2} - w + 7]$ $-2e^{3} + 14e + 6$
73 $[73, 73, -6w^{2} + 4w + 25]$ $\phantom{-}e^{4} - 7e^{2} + 4e + 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
11 $[11, 11, w^{2} - w - 1]$ $-1$