Properties

Base field \(\Q(\sqrt{61}) \)
Weight [2, 2]
Level norm 61
Level $[61, 61, 2w - 1]$
Label 2.2.61.1-61.1-a
Dimension 1
CM no
Base change yes

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Base field \(\Q(\sqrt{61}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 15\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2]
Level $[61, 61, 2w - 1]$
Label 2.2.61.1-61.1-a
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 56

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, -w - 3]$ $-2$
3 $[3, 3, -w + 4]$ $-2$
4 $[4, 2, 2]$ $-3$
5 $[5, 5, w - 5]$ $-3$
5 $[5, 5, -w - 4]$ $-3$
13 $[13, 13, -w - 1]$ $\phantom{-}1$
13 $[13, 13, w - 2]$ $\phantom{-}1$
19 $[19, 19, 3w - 14]$ $-4$
19 $[19, 19, -3w - 11]$ $-4$
41 $[41, 41, -w - 7]$ $\phantom{-}5$
41 $[41, 41, w - 8]$ $\phantom{-}5$
47 $[47, 47, 3w - 11]$ $\phantom{-}4$
47 $[47, 47, -3w - 8]$ $\phantom{-}4$
49 $[49, 7, -7]$ $-13$
61 $[61, 61, 2w - 1]$ $-1$
73 $[73, 73, -3w + 16]$ $-11$
73 $[73, 73, 3w + 13]$ $-11$
83 $[83, 83, 2w - 13]$ $\phantom{-}4$
83 $[83, 83, -2w - 11]$ $\phantom{-}4$
97 $[97, 97, 7w + 22]$ $-14$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
61 $[61, 61, 2w - 1]$ $1$