Properties

Label 2.2.57.1-19.1-b
Base field \(\Q(\sqrt{57}) \)
Weight $[2, 2]$
Level norm $19$
Level $[19, 19, 10w + 33]$
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: $[19, 19, 10w + 33]$
Dimension: $1$
CM: no
Base change: yes
Newspace dimension: $22$

Hecke eigenvalues ($q$-expansion)

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

Atkin-Lehner eigenvalues

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