Properties

Base field \(\Q(\sqrt{10}) \)
Weight [2, 2]
Level norm 338
Level $[338, 26, 13w]$
Label 2.2.40.1-338.1-g
Dimension 1
CM no
Base change yes

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Base field \(\Q(\sqrt{10}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 10\); narrow class number \(2\) and class number \(2\).

Form

Weight [2, 2]
Level $[338, 26, 13w]$
Label 2.2.40.1-338.1-g
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 170

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}1$
3 $[3, 3, w + 1]$ $-3$
3 $[3, 3, w + 2]$ $-3$
5 $[5, 5, w]$ $-1$
13 $[13, 13, w + 6]$ $-1$
13 $[13, 13, w + 7]$ $-1$
31 $[31, 31, -2w + 3]$ $\phantom{-}4$
31 $[31, 31, 2w + 3]$ $\phantom{-}4$
37 $[37, 37, w + 11]$ $\phantom{-}3$
37 $[37, 37, w + 26]$ $\phantom{-}3$
41 $[41, 41, 3w + 7]$ $\phantom{-}0$
41 $[41, 41, -3w + 7]$ $\phantom{-}0$
43 $[43, 43, w + 15]$ $-5$
43 $[43, 43, w + 28]$ $-5$
49 $[49, 7, -7]$ $-13$
53 $[53, 53, w + 13]$ $\phantom{-}12$
53 $[53, 53, w + 40]$ $\phantom{-}12$
67 $[67, 67, w + 12]$ $-2$
67 $[67, 67, w + 55]$ $-2$
71 $[71, 71, -w - 9]$ $-5$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $-1$
13 $[13, 13, w + 6]$ $1$
13 $[13, 13, w + 7]$ $1$