Properties

Label 5.5.157457.1-29.2-b
Base field 5.5.157457.1
Weight $[2, 2, 2, 2, 2]$
Level norm $29$
Level $[29, 29, -w^{2} + 2w + 3]$
Dimension $1$
CM no
Base change no

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Base field 5.5.157457.1

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

Form

Weight: $[2, 2, 2, 2, 2]$
Level: $[29, 29, -w^{2} + 2w + 3]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $46$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w - 1]$ $\phantom{-}0$
5 $[5, 5, w^{2} - w - 2]$ $\phantom{-}4$
7 $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 4w + 2]$ $-2$
13 $[13, 13, w^{3} - 2w^{2} - 2w + 2]$ $\phantom{-}1$
29 $[29, 29, -w^{4} + 3w^{3} + 2w^{2} - 7w - 1]$ $\phantom{-}2$
29 $[29, 29, -w^{2} + 2w + 3]$ $\phantom{-}1$
31 $[31, 31, w^{4} - 2w^{3} - 3w^{2} + 5w]$ $\phantom{-}3$
31 $[31, 31, w^{3} - 2w^{2} - 3w + 2]$ $\phantom{-}5$
32 $[32, 2, 2]$ $-1$
43 $[43, 43, -w^{2} - w + 4]$ $\phantom{-}5$
53 $[53, 53, -w^{4} + w^{3} + 6w^{2} - 2w - 5]$ $-3$
53 $[53, 53, -w^{4} + 2w^{3} + 4w^{2} - 5w - 2]$ $\phantom{-}3$
73 $[73, 73, w^{4} - w^{3} - 6w^{2} + 2w + 6]$ $\phantom{-}8$
73 $[73, 73, w^{3} - w^{2} - 4w + 2]$ $-14$
81 $[81, 3, 2w^{4} - 5w^{3} - 4w^{2} + 9w + 2]$ $-17$
83 $[83, 83, w^{3} - w^{2} - 5w]$ $\phantom{-}14$
89 $[89, 89, -w^{4} + 2w^{3} + 4w^{2} - 4w - 2]$ $\phantom{-}10$
97 $[97, 97, w^{4} - 3w^{3} - 2w^{2} + 6w + 2]$ $-12$
101 $[101, 101, -w^{4} + 3w^{3} + 3w^{2} - 7w - 3]$ $\phantom{-}10$
103 $[103, 103, -w^{4} + w^{3} + 6w^{2} - w - 7]$ $\phantom{-}13$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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