Properties

Label 4.4.16357.1-25.3-e
Base field 4.4.16357.1
Weight $[2, 2, 2, 2]$
Level norm $25$
Level $[25, 25, w^{3} - 7w + 1]$
Dimension $1$
CM no
Base change no

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Base field 4.4.16357.1

Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - x + 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[25, 25, w^{3} - 7w + 1]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $42$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $-2$
5 $[5, 5, -w^{3} + 5w + 2]$ $\phantom{-}3$
5 $[5, 5, w - 1]$ $\phantom{-}0$
11 $[11, 11, -w^{3} + 5w]$ $\phantom{-}6$
13 $[13, 13, -w^{3} + w^{2} + 6w - 3]$ $-3$
16 $[16, 2, 2]$ $-3$
19 $[19, 19, 2w^{3} - w^{2} - 11w + 2]$ $\phantom{-}2$
25 $[25, 5, -w^{2} + w + 3]$ $\phantom{-}6$
27 $[27, 3, w^{3} - w^{2} - 5w + 4]$ $\phantom{-}8$
31 $[31, 31, -w - 3]$ $-6$
37 $[37, 37, -w^{3} - w^{2} + 6w + 4]$ $-3$
41 $[41, 41, w^{3} + w^{2} - 6w - 5]$ $-6$
43 $[43, 43, w^{3} - 7w - 2]$ $-8$
47 $[47, 47, -2w^{3} + 11w + 2]$ $\phantom{-}12$
61 $[61, 61, w^{2} - 3]$ $\phantom{-}10$
67 $[67, 67, w^{2} + w - 4]$ $\phantom{-}12$
79 $[79, 79, -4w^{3} + 2w^{2} + 22w - 9]$ $\phantom{-}10$
97 $[97, 97, -3w^{3} + 2w^{2} + 19w - 6]$ $\phantom{-}15$
97 $[97, 97, -w^{3} + 6w - 3]$ $\phantom{-}15$
97 $[97, 97, -3w^{3} + 16w]$ $\phantom{-}6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, w - 1]$ $1$