Properties

Base field \(\Q(\sqrt{37}) \)
Weight [2, 2]
Level norm 196
Level $[196, 14, 14]$
Label 2.2.37.1-196.1-h
Dimension 1
CM no
Base change yes

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Base field \(\Q(\sqrt{37}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 9\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2]
Level $[196, 14, 14]$
Label 2.2.37.1-196.1-h
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 45

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, -w + 3]$ $-2$
3 $[3, 3, -w - 2]$ $-2$
4 $[4, 2, 2]$ $\phantom{-}1$
7 $[7, 7, w + 1]$ $\phantom{-}1$
7 $[7, 7, -w + 2]$ $\phantom{-}1$
11 $[11, 11, w + 4]$ $\phantom{-}0$
11 $[11, 11, -w + 5]$ $\phantom{-}0$
25 $[25, 5, 5]$ $-10$
37 $[37, 37, 2w - 1]$ $\phantom{-}2$
41 $[41, 41, 3w - 8]$ $\phantom{-}6$
41 $[41, 41, 3w + 5]$ $\phantom{-}6$
47 $[47, 47, -w - 7]$ $-12$
47 $[47, 47, w - 8]$ $-12$
53 $[53, 53, -3w - 4]$ $\phantom{-}6$
53 $[53, 53, 3w - 7]$ $\phantom{-}6$
67 $[67, 67, 4w - 11]$ $-4$
67 $[67, 67, 4w + 7]$ $-4$
71 $[71, 71, 3w - 5]$ $\phantom{-}0$
71 $[71, 71, -3w - 2]$ $\phantom{-}0$
73 $[73, 73, -3w - 11]$ $\phantom{-}2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $-1$
7 $[7, 7, w + 1]$ $-1$
7 $[7, 7, -w + 2]$ $-1$