Properties

Base field 4.4.8069.1
Weight [2, 2, 2, 2]
Level norm 29
Level $[29, 29, 2w^{3} - w^{2} - 9w + 5]$
Label 4.4.8069.1-29.1-d
Dimension 6
CM no
Base change no

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Base field 4.4.8069.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 5x + 1\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[29, 29, 2w^{3} - w^{2} - 9w + 5]$
Label 4.4.8069.1-29.1-d
Dimension 6
Is CM no
Is base change no
Parent newspace dimension 16

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} \) \(\mathstrut +\mathstrut 11x^{5} \) \(\mathstrut +\mathstrut 40x^{4} \) \(\mathstrut +\mathstrut 40x^{3} \) \(\mathstrut -\mathstrut 62x^{2} \) \(\mathstrut -\mathstrut 133x \) \(\mathstrut -\mathstrut 51\)

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Norm Prime Eigenvalue
5 $[5, 5, w^{3} - 4w]$ $\phantom{-}e$
7 $[7, 7, w + 1]$ $\phantom{-}e^{5} + 8e^{4} + 17e^{3} - 5e^{2} - 41e - 24$
7 $[7, 7, -w^{3} + 4w - 1]$ $-e^{4} - 5e^{3} - 2e^{2} + 11e + 6$
13 $[13, 13, -w^{2} + 3]$ $-e^{5} - 8e^{4} - 16e^{3} + 9e^{2} + 39e + 12$
16 $[16, 2, 2]$ $\phantom{-}e^{5} + 7e^{4} + 12e^{3} - 8e^{2} - 32e - 11$
17 $[17, 17, w^{3} + w^{2} - 4w - 2]$ $\phantom{-}e^{5} + 9e^{4} + 22e^{3} - 4e^{2} - 55e - 30$
17 $[17, 17, -w^{3} + 5w - 2]$ $\phantom{-}e^{2} + 3e$
19 $[19, 19, -w^{2} - w + 4]$ $-e^{3} - 4e^{2} + 2e + 10$
19 $[19, 19, -w^{2} - w + 1]$ $-e^{5} - 8e^{4} - 17e^{3} + 6e^{2} + 44e + 18$
29 $[29, 29, 2w^{3} - w^{2} - 9w + 5]$ $\phantom{-}1$
41 $[41, 41, -w^{3} + w^{2} + 5w - 3]$ $-3e^{5} - 24e^{4} - 51e^{3} + 16e^{2} + 123e + 60$
43 $[43, 43, w^{3} - w^{2} - 4w + 2]$ $\phantom{-}e^{5} + 9e^{4} + 20e^{3} - 12e^{2} - 52e - 12$
43 $[43, 43, w^{3} - 6w]$ $\phantom{-}e^{4} + 5e^{3} - 17e - 4$
47 $[47, 47, -w^{3} - w^{2} + 5w]$ $\phantom{-}e^{5} + 11e^{4} + 33e^{3} + 5e^{2} - 74e - 48$
49 $[49, 7, w^{2} + 2w - 2]$ $\phantom{-}e^{5} + 11e^{4} + 34e^{3} + 7e^{2} - 80e - 53$
59 $[59, 59, 2w^{3} - 8w + 3]$ $\phantom{-}2e^{5} + 16e^{4} + 32e^{3} - 18e^{2} - 77e - 21$
67 $[67, 67, w^{2} - w - 4]$ $-4e^{5} - 33e^{4} - 73e^{3} + 20e^{2} + 176e + 84$
79 $[79, 79, w^{3} - w^{2} - 4w + 1]$ $-e^{5} - 5e^{4} - e^{3} + 14e^{2} + 3e - 3$
81 $[81, 3, -3]$ $-3e^{5} - 24e^{4} - 50e^{3} + 18e^{2} + 119e + 64$
97 $[97, 97, w^{3} + w^{2} - 5w + 1]$ $-e^{4} - 7e^{3} - 8e^{2} + 15e + 10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
29 $[29, 29, 2w^{3} - w^{2} - 9w + 5]$ $-1$