Properties

Label 4.4.12197.1-25.3-d
Base field 4.4.12197.1
Weight $[2, 2, 2, 2]$
Level norm $25$
Level $[25, 25, -w^{3} + w^{2} + 5w - 1]$
Dimension $1$
CM no
Base change no

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Base field 4.4.12197.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[25, 25, -w^{3} + w^{2} + 5w - 1]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $23$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
5 $[5, 5, w + 1]$ $\phantom{-}4$
5 $[5, 5, -w + 2]$ $\phantom{-}0$
11 $[11, 11, w^{3} - w^{2} - 4w + 2]$ $\phantom{-}2$
13 $[13, 13, w^{3} - w^{2} - 4w]$ $\phantom{-}1$
16 $[16, 2, 2]$ $\phantom{-}3$
17 $[17, 17, -w^{2} + w + 3]$ $\phantom{-}3$
19 $[19, 19, w^{3} - 5w]$ $\phantom{-}0$
19 $[19, 19, -w + 3]$ $-5$
23 $[23, 23, 2w^{3} - 2w^{2} - 9w + 4]$ $-4$
23 $[23, 23, w^{2} - 2]$ $\phantom{-}1$
25 $[25, 5, w^{2} - 3]$ $-4$
37 $[37, 37, -w^{3} + 2w^{2} + 4w - 6]$ $\phantom{-}7$
37 $[37, 37, -w^{3} + w^{2} + 6w - 4]$ $\phantom{-}7$
41 $[41, 41, w^{2} - w - 5]$ $\phantom{-}8$
47 $[47, 47, w^{3} - 6w + 1]$ $\phantom{-}3$
61 $[61, 61, -w^{3} + w^{2} + 6w - 2]$ $\phantom{-}8$
67 $[67, 67, 2w^{3} - w^{2} - 9w + 2]$ $-3$
67 $[67, 67, w^{3} - 7w + 3]$ $-7$
73 $[73, 73, 2w^{3} - w^{2} - 9w]$ $\phantom{-}6$
81 $[81, 3, -3]$ $-7$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, -w + 2]$ $1$