Properties

Base field 3.3.316.1
Weight [2, 2, 2]
Level norm 29
Level $[29, 29, 2w + 1]$
Label 3.3.316.1-29.1-d
Dimension 3
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 $[29, 29, 2w + 1]$
Label 3.3.316.1-29.1-d
Dimension 3
Is CM no
Is base change no
Parent newspace dimension 9

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} \) \(\mathstrut +\mathstrut 2x^{2} \) \(\mathstrut -\mathstrut x \) \(\mathstrut -\mathstrut 1\)

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

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
29 $[29, 29, 2w + 1]$ $1$