Properties

Label 5.5.179024.1-3.1-b
Base field 5.5.179024.1
Weight $[2, 2, 2, 2, 2]$
Level norm $3$
Level $[3, 3, 2w^{4} + w^{3} - 15w^{2} - 7w + 7]$
Dimension $1$
CM no
Base change no

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Base field 5.5.179024.1

Generator \(w\), with minimal polynomial \(x^{5} - 8x^{3} + 6x - 2\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2]$
Level: $[3, 3, 2w^{4} + w^{3} - 15w^{2} - 7w + 7]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}0$
3 $[3, 3, 2w^{4} + w^{3} - 15w^{2} - 7w + 7]$ $-1$
11 $[11, 11, 2w^{4} + w^{3} - 16w^{2} - 9w + 9]$ $\phantom{-}0$
17 $[17, 17, w^{4} + w^{3} - 8w^{2} - 6w + 5]$ $\phantom{-}6$
29 $[29, 29, w^{4} - 8w^{2} + 3]$ $-6$
43 $[43, 43, 6w^{4} + 3w^{3} - 46w^{2} - 24w + 21]$ $\phantom{-}4$
43 $[43, 43, 2w^{4} + w^{3} - 15w^{2} - 6w + 7]$ $-8$
47 $[47, 47, 3w^{4} + w^{3} - 23w^{2} - 9w + 11]$ $-12$
47 $[47, 47, w^{4} + w^{3} - 8w^{2} - 7w + 3]$ $-12$
49 $[49, 7, -w^{4} + 8w^{2} + 2w - 5]$ $-2$
53 $[53, 53, -6w^{4} - 3w^{3} + 46w^{2} + 23w - 23]$ $-6$
53 $[53, 53, 2w^{4} + w^{3} - 15w^{2} - 7w + 5]$ $-6$
59 $[59, 59, 13w^{4} + 7w^{3} - 101w^{2} - 54w + 55]$ $\phantom{-}12$
67 $[67, 67, 5w^{4} + 3w^{3} - 39w^{2} - 23w + 19]$ $\phantom{-}4$
67 $[67, 67, 4w^{4} + 2w^{3} - 32w^{2} - 16w + 19]$ $-8$
71 $[71, 71, 4w^{4} + 3w^{3} - 31w^{2} - 22w + 15]$ $\phantom{-}0$
71 $[71, 71, 9w^{4} + 5w^{3} - 70w^{2} - 38w + 39]$ $\phantom{-}12$
71 $[71, 71, 4w^{4} + w^{3} - 31w^{2} - 8w + 17]$ $-12$
81 $[81, 3, -5w^{4} - 2w^{3} + 38w^{2} + 17w - 19]$ $\phantom{-}2$
83 $[83, 83, -3w^{4} - w^{3} + 24w^{2} + 9w - 13]$ $-12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, 2w^{4} + w^{3} - 15w^{2} - 7w + 7]$ $1$