Properties

Base field 4.4.6125.1
Weight [2, 2, 2, 2]
Level norm 19
Level $[19,19,-2w^{3} - 2w^{2} + 13w + 6]$
Label 4.4.6125.1-19.2-a
Dimension 2
CM no
Base change no

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Base field 4.4.6125.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 9x^{2} + 9x + 11\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[19,19,-2w^{3} - 2w^{2} + 13w + 6]$
Label 4.4.6125.1-19.2-a
Dimension 2
Is CM no
Is base change no
Parent newspace dimension 4

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 4x + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -2w^{3} - 2w^{2} + 13w + 8]$ $\phantom{-}e$
11 $[11, 11, 2w^{3} + 3w^{2} - 12w - 11]$ $-2e + 3$
11 $[11, 11, -w^{3} - 2w^{2} + 6w + 9]$ $\phantom{-}2$
11 $[11, 11, w^{3} + w^{2} - 7w - 4]$ $-4$
11 $[11, 11, w - 1]$ $\phantom{-}e$
16 $[16, 2, 2]$ $\phantom{-}e - 4$
19 $[19, 19, -w^{2} + 4]$ $\phantom{-}e + 2$
19 $[19, 19, 2w^{3} + 2w^{2} - 13w - 6]$ $-1$
19 $[19, 19, 3w^{3} + 4w^{2} - 18w - 16]$ $-2e + 8$
19 $[19, 19, -w^{3} - w^{2} + 5w + 3]$ $-2e + 5$
49 $[49, 7, 2w^{3} + 3w^{2} - 13w - 15]$ $-4$
59 $[59, 59, -3w^{3} - 4w^{2} + 19w + 14]$ $-4e + 8$
59 $[59, 59, 3w^{3} + 4w^{2} - 18w - 17]$ $-e + 2$
59 $[59, 59, 2w^{3} + 3w^{2} - 11w - 13]$ $\phantom{-}2e + 2$
59 $[59, 59, -w^{3} - 2w^{2} + 7w + 9]$ $\phantom{-}4e - 2$
71 $[71, 71, 3w^{3} + 3w^{2} - 17w - 10]$ $\phantom{-}e - 2$
71 $[71, 71, -2w^{3} - w^{2} + 14w + 2]$ $\phantom{-}2e + 2$
71 $[71, 71, 5w^{3} + 7w^{2} - 30w - 25]$ $-4e + 14$
71 $[71, 71, -3w^{3} - 4w^{2} + 16w + 16]$ $\phantom{-}2e + 2$
81 $[81, 3, -3]$ $-4e + 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
19 $[19,19,-2w^{3} - 2w^{2} + 13w + 6]$ $1$