Properties

Base field \(\Q(\sqrt{19}) \)
Weight [2, 2]
Level norm 38
Level $[38, 38, -13w - 57]$
Label 2.2.76.1-38.1-h
Dimension 1
CM no
Base change yes

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Base field \(\Q(\sqrt{19}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 19\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2]
Level $[38, 38, -13w - 57]$
Label 2.2.76.1-38.1-h
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 28

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -3w - 13]$ $\phantom{-}1$
3 $[3, 3, w + 4]$ $-1$
3 $[3, 3, w - 4]$ $-1$
5 $[5, 5, 2w + 9]$ $-4$
5 $[5, 5, -2w + 9]$ $-4$
17 $[17, 17, w + 6]$ $\phantom{-}3$
17 $[17, 17, -w + 6]$ $\phantom{-}3$
19 $[19, 19, w]$ $-1$
31 $[31, 31, 20w + 87]$ $-8$
31 $[31, 31, 7w + 30]$ $-8$
49 $[49, 7, -7]$ $-5$
59 $[59, 59, 6w + 25]$ $\phantom{-}15$
59 $[59, 59, -6w + 25]$ $\phantom{-}15$
61 $[61, 61, -9w - 40]$ $\phantom{-}2$
61 $[61, 61, 9w - 40]$ $\phantom{-}2$
67 $[67, 67, 2w - 3]$ $\phantom{-}3$
67 $[67, 67, -2w - 3]$ $\phantom{-}3$
71 $[71, 71, 3w + 10]$ $\phantom{-}2$
71 $[71, 71, 3w - 10]$ $\phantom{-}2$
73 $[73, 73, 27w + 118]$ $\phantom{-}9$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -3w - 13]$ $-1$
19 $[19, 19, w]$ $1$