Properties

Base field \(\Q(\sqrt{51}) \)
Weight [2, 2]
Level norm 34
Level $[34, 34, w + 17]$
Label 2.2.204.1-34.1-a
Dimension 1
CM no
Base change yes

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Base field \(\Q(\sqrt{51}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 51\); narrow class number \(4\) and class number \(2\).

Form

Weight [2, 2]
Level $[34, 34, w + 17]$
Label 2.2.204.1-34.1-a
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 220

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w + 7]$ $\phantom{-}1$
3 $[3, 3, w]$ $-2$
5 $[5, 5, w + 1]$ $\phantom{-}0$
5 $[5, 5, w + 4]$ $\phantom{-}0$
7 $[7, 7, w + 3]$ $-4$
7 $[7, 7, w + 4]$ $-4$
13 $[13, 13, w - 8]$ $\phantom{-}2$
13 $[13, 13, w + 8]$ $\phantom{-}2$
17 $[17, 17, w]$ $-1$
29 $[29, 29, w + 14]$ $\phantom{-}0$
29 $[29, 29, w + 15]$ $\phantom{-}0$
31 $[31, 31, w + 12]$ $-4$
31 $[31, 31, w + 19]$ $-4$
41 $[41, 41, w + 16]$ $\phantom{-}6$
41 $[41, 41, w + 25]$ $\phantom{-}6$
47 $[47, 47, -w - 2]$ $\phantom{-}0$
47 $[47, 47, w - 2]$ $\phantom{-}0$
59 $[59, 59, 3w - 20]$ $\phantom{-}0$
59 $[59, 59, 10w - 71]$ $\phantom{-}0$
79 $[79, 79, w + 29]$ $\phantom{-}8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 7]$ $-1$
17 $[17, 17, w]$ $1$