Properties

Label 2.2.120.1-20.1-a
Base field \(\Q(\sqrt{30}) \)
Weight $[2, 2]$
Level norm $20$
Level $[20, 10, -2w + 10]$
Dimension $1$
CM no
Base change yes

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Base field \(\Q(\sqrt{30}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 30\); narrow class number \(4\) and class number \(2\).

Form

Weight: $[2, 2]$
Level: $[20, 10, -2w + 10]$
Dimension: $1$
CM: no
Base change: yes
Newspace dimension: $16$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}0$
3 $[3, 3, w]$ $\phantom{-}2$
5 $[5, 5, -w + 5]$ $\phantom{-}1$
7 $[7, 7, w + 3]$ $\phantom{-}2$
7 $[7, 7, w + 4]$ $\phantom{-}2$
13 $[13, 13, w + 2]$ $\phantom{-}2$
13 $[13, 13, w + 11]$ $\phantom{-}2$
17 $[17, 17, w + 8]$ $\phantom{-}6$
17 $[17, 17, w + 9]$ $\phantom{-}6$
19 $[19, 19, w + 7]$ $-4$
19 $[19, 19, -w + 7]$ $-4$
29 $[29, 29, -w - 1]$ $-6$
29 $[29, 29, w - 1]$ $-6$
37 $[37, 37, w + 17]$ $\phantom{-}2$
37 $[37, 37, w + 20]$ $\phantom{-}2$
71 $[71, 71, 2w - 7]$ $\phantom{-}12$
71 $[71, 71, -2w - 7]$ $\phantom{-}12$
83 $[83, 83, w + 14]$ $-6$
83 $[83, 83, w + 69]$ $-6$
101 $[101, 101, -7w + 37]$ $-6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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