Properties

Label 2.2.40.1-360.1-p
Base field \(\Q(\sqrt{10}) \)
Weight $[2, 2]$
Level norm $360$
Level $[360, 60, 6w]$
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: $[360, 60, 6w]$
Dimension: $1$
CM: no
Base change: yes
Newspace dimension: $56$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}0$
3 $[3, 3, w + 1]$ $\phantom{-}1$
3 $[3, 3, w + 2]$ $\phantom{-}1$
5 $[5, 5, w]$ $\phantom{-}1$
13 $[13, 13, w + 6]$ $\phantom{-}6$
13 $[13, 13, w + 7]$ $\phantom{-}6$
31 $[31, 31, -2w + 3]$ $-8$
31 $[31, 31, 2w + 3]$ $-8$
37 $[37, 37, w + 11]$ $-2$
37 $[37, 37, w + 26]$ $-2$
41 $[41, 41, 3w + 7]$ $-6$
41 $[41, 41, -3w + 7]$ $-6$
43 $[43, 43, w + 15]$ $\phantom{-}12$
43 $[43, 43, w + 28]$ $\phantom{-}12$
49 $[49, 7, -7]$ $-14$
53 $[53, 53, w + 13]$ $\phantom{-}6$
53 $[53, 53, w + 40]$ $\phantom{-}6$
67 $[67, 67, w + 12]$ $\phantom{-}4$
67 $[67, 67, w + 55]$ $\phantom{-}4$
71 $[71, 71, -w - 9]$ $\phantom{-}8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w]$ $-1$
$3$ $[3, 3, w + 1]$ $-1$
$3$ $[3, 3, w + 2]$ $-1$
$5$ $[5, 5, w]$ $-1$