Properties

Base field \(\Q(\sqrt{57}) \)
Weight [2, 2]
Level norm 57
Level $[57, 57, -2w + 1]$
Label 2.2.57.1-57.1-f
Dimension 1
CM no
Base change yes

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Base field \(\Q(\sqrt{57}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 14\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2]
Level $[57, 57, -2w + 1]$
Label 2.2.57.1-57.1-f
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 42

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w + 4]$ $-2$
2 $[2, 2, -w - 3]$ $-2$
3 $[3, 3, -4w - 13]$ $-1$
7 $[7, 7, -2w - 7]$ $-5$
7 $[7, 7, -2w + 9]$ $-5$
19 $[19, 19, 10w + 33]$ $-1$
25 $[25, 5, 5]$ $-1$
29 $[29, 29, -6w - 19]$ $-2$
29 $[29, 29, -6w + 25]$ $-2$
41 $[41, 41, 2w - 5]$ $\phantom{-}0$
41 $[41, 41, -2w - 3]$ $\phantom{-}0$
43 $[43, 43, 2w - 11]$ $-1$
43 $[43, 43, 2w + 9]$ $-1$
53 $[53, 53, 2w - 3]$ $\phantom{-}10$
53 $[53, 53, -2w - 1]$ $\phantom{-}10$
59 $[59, 59, 4w - 15]$ $-8$
59 $[59, 59, 4w + 11]$ $-8$
61 $[61, 61, -4w - 15]$ $-1$
61 $[61, 61, -4w + 19]$ $-1$
71 $[71, 71, 8w + 25]$ $-12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -4w - 13]$ $1$
19 $[19, 19, 10w + 33]$ $1$