Properties

Base field 4.4.9909.1
Weight [2, 2, 2, 2]
Level norm 13
Level $[13, 13, -w^{3} + w^{2} + 3w - 1]$
Label 4.4.9909.1-13.1-a
Dimension 1
CM no
Base change no

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Base field 4.4.9909.1

Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 3x + 3\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[13, 13, -w^{3} + w^{2} + 3w - 1]$
Label 4.4.9909.1-13.1-a
Dimension 1
Is CM no
Is base change no
Parent newspace dimension 14

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w]$ $-2$
5 $[5, 5, w - 1]$ $\phantom{-}3$
7 $[7, 7, w^{3} - w^{2} - 4w + 1]$ $-1$
11 $[11, 11, -w^{2} + w + 2]$ $-3$
13 $[13, 13, -w^{3} + w^{2} + 3w - 1]$ $\phantom{-}1$
16 $[16, 2, 2]$ $-1$
17 $[17, 17, -w^{3} + 5w + 2]$ $-3$
29 $[29, 29, -w^{2} + w + 1]$ $\phantom{-}0$
37 $[37, 37, -w^{3} + 2w^{2} + 4w - 4]$ $-7$
41 $[41, 41, -w^{3} + w^{2} + 5w + 1]$ $\phantom{-}9$
41 $[41, 41, w^{2} - 5]$ $-9$
47 $[47, 47, w^{3} - w^{2} - 5w - 2]$ $-3$
47 $[47, 47, -w^{3} + 2w^{2} + 4w - 1]$ $\phantom{-}3$
53 $[53, 53, w^{3} - 4w - 4]$ $\phantom{-}6$
53 $[53, 53, 2w^{3} - 2w^{2} - 9w + 1]$ $-6$
61 $[61, 61, -w^{3} + w^{2} + 6w - 2]$ $-10$
71 $[71, 71, w^{3} - w^{2} - 6w - 2]$ $\phantom{-}6$
103 $[103, 103, 2w^{3} - 2w^{2} - 8w + 1]$ $-4$
103 $[103, 103, -3w^{3} + 3w^{2} + 13w - 5]$ $-4$
109 $[109, 109, 2w^{3} - w^{2} - 8w - 4]$ $\phantom{-}2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
13 $[13, 13, -w^{3} + w^{2} + 3w - 1]$ $-1$