Properties

Label 4.4.13725.1-19.4-c
Base field 4.4.13725.1
Weight $[2, 2, 2, 2]$
Level norm $19$
Level $[19,19,-3w^{3} + 10w^{2} + 17w - 43]$
Dimension $1$
CM no
Base change no

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Base field 4.4.13725.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 13x^{2} + x + 31\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[19,19,-3w^{3} + 10w^{2} + 17w - 43]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $22$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
9 $[9, 3, -2w^{3} + 6w^{2} + 13w - 26]$ $\phantom{-}3$
11 $[11, 11, w^{2} - w - 8]$ $\phantom{-}3$
11 $[11, 11, -4w^{3} + 13w^{2} + 23w - 55]$ $\phantom{-}0$
16 $[16, 2, 2]$ $-1$
19 $[19, 19, -w - 1]$ $\phantom{-}0$
19 $[19, 19, -w^{3} + 3w^{2} + 7w - 14]$ $\phantom{-}6$
19 $[19, 19, w^{3} - 4w^{2} - 5w + 20]$ $\phantom{-}7$
19 $[19, 19, -3w^{3} + 10w^{2} + 17w - 43]$ $-1$
25 $[25, 5, -w^{3} + 3w^{2} + 6w - 10]$ $\phantom{-}6$
29 $[29, 29, 4w^{3} - 13w^{2} - 23w + 57]$ $-3$
29 $[29, 29, w^{2} - w - 6]$ $\phantom{-}0$
31 $[31, 31, -2w^{3} + 7w^{2} + 11w - 31]$ $-3$
31 $[31, 31, -2w^{3} + 7w^{2} + 11w - 32]$ $\phantom{-}6$
41 $[41, 41, 3w^{3} - 10w^{2} - 18w + 43]$ $-3$
41 $[41, 41, 3w^{3} - 9w^{2} - 19w + 37]$ $\phantom{-}9$
41 $[41, 41, 2w^{3} - 6w^{2} - 11w + 24]$ $-12$
41 $[41, 41, -2w^{3} + 7w^{2} + 12w - 33]$ $\phantom{-}9$
59 $[59, 59, 3w^{3} - 10w^{2} - 17w + 46]$ $-12$
59 $[59, 59, -w^{3} + 4w^{2} + 5w - 17]$ $\phantom{-}0$
61 $[61, 61, 4w^{3} - 12w^{2} - 25w + 50]$ $\phantom{-}1$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19,19,-3w^{3} + 10w^{2} + 17w - 43]$ $1$