Properties

Base field \(\Q(\sqrt{30}) \)
Weight [2, 2]
Level norm 30
Level $[30, 30, w]$
Label 2.2.120.1-30.1-i
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 $[30, 30, w]$
Label 2.2.120.1-30.1-i
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 44

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w]$ $-1$
3 $[3, 3, w]$ $\phantom{-}1$
5 $[5, 5, -w + 5]$ $-1$
7 $[7, 7, w + 3]$ $-4$
7 $[7, 7, w + 4]$ $-4$
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 $[71, 71, 2w - 7]$ $\phantom{-}0$
71 $[71, 71, -2w - 7]$ $\phantom{-}0$
83 $[83, 83, w + 14]$ $\phantom{-}12$
83 $[83, 83, w + 69]$ $\phantom{-}12$
101 $[101, 101, -7w + 37]$ $\phantom{-}18$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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