Properties

Base field 5.5.36497.1
Weight [2, 2, 2, 2, 2]
Level norm 25
Level $[25, 5, -w^{2} + 2w + 2]$
Label 5.5.36497.1-25.1-b
Dimension 1
CM no
Base change no

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Base field 5.5.36497.1

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

Form

Weight [2, 2, 2, 2, 2]
Level $[25, 5, -w^{2} + 2w + 2]$
Label 5.5.36497.1-25.1-b
Dimension 1
Is CM no
Is base change no
Parent newspace dimension 4

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w^{4} - 2w^{3} - 3w^{2} + 4w + 1]$ $\phantom{-}3$
13 $[13, 13, w^{3} - 2w^{2} - 2w + 2]$ $\phantom{-}3$
23 $[23, 23, 2w^{4} - 3w^{3} - 6w^{2} + 5w + 1]$ $-3$
25 $[25, 5, -w^{2} + 2w + 2]$ $\phantom{-}1$
29 $[29, 29, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $\phantom{-}2$
31 $[31, 31, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ $\phantom{-}5$
32 $[32, 2, 2]$ $-9$
37 $[37, 37, w^{4} - 2w^{3} - 2w^{2} + 4w + 1]$ $\phantom{-}1$
47 $[47, 47, w^{4} - w^{3} - 5w^{2} + 2w + 3]$ $-12$
47 $[47, 47, 2w^{4} - 3w^{3} - 6w^{2} + 6w + 2]$ $-10$
49 $[49, 7, -w^{4} + 2w^{3} + 4w^{2} - 6w - 2]$ $\phantom{-}3$
53 $[53, 53, -2w^{4} + 3w^{3} + 7w^{2} - 7w - 2]$ $\phantom{-}4$
59 $[59, 59, -2w^{4} + 3w^{3} + 6w^{2} - 5w - 2]$ $-8$
67 $[67, 67, -w^{4} + 3w^{3} + 2w^{2} - 7w]$ $\phantom{-}6$
67 $[67, 67, -w^{4} + 3w^{3} + w^{2} - 7w + 1]$ $-8$
71 $[71, 71, w^{4} - 2w^{3} - 4w^{2} + 3w + 3]$ $\phantom{-}7$
71 $[71, 71, -w^{2} + 5]$ $-6$
79 $[79, 79, 2w^{4} - 3w^{3} - 5w^{2} + 3w + 1]$ $\phantom{-}6$
81 $[81, 3, -w^{4} + 3w^{3} + 3w^{2} - 8w - 2]$ $\phantom{-}10$
83 $[83, 83, -3w^{4} + 3w^{3} + 10w^{2} - 2w - 2]$ $-12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
25 $[25, 5, -w^{2} + 2w + 2]$ $-1$