Properties

Base field \(\Q(\sqrt{15}) \)
Weight [2, 2]
Level norm 147
Level $[147, 21, 7w]$
Label 2.2.60.1-147.1-a
Dimension 1
CM no
Base change yes

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Base field \(\Q(\sqrt{15}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 15\); narrow class number \(4\) and class number \(2\).

Form

Weight [2, 2]
Level $[147, 21, 7w]$
Label 2.2.60.1-147.1-a
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 132

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}1$
3 $[3, 3, w]$ $\phantom{-}1$
5 $[5, 5, w]$ $\phantom{-}2$
7 $[7, 7, w + 1]$ $-1$
7 $[7, 7, w + 6]$ $-1$
11 $[11, 11, -w - 2]$ $-4$
11 $[11, 11, w - 2]$ $-4$
17 $[17, 17, w + 7]$ $\phantom{-}6$
17 $[17, 17, w + 10]$ $\phantom{-}6$
43 $[43, 43, w + 12]$ $-4$
43 $[43, 43, w + 31]$ $-4$
53 $[53, 53, w + 11]$ $-6$
53 $[53, 53, w + 42]$ $-6$
59 $[59, 59, 2w - 1]$ $-12$
59 $[59, 59, -2w - 1]$ $-12$
61 $[61, 61, 2w - 11]$ $-2$
61 $[61, 61, -2w - 11]$ $-2$
67 $[67, 67, w + 22]$ $\phantom{-}4$
67 $[67, 67, w + 45]$ $\phantom{-}4$
71 $[71, 71, 3w - 8]$ $\phantom{-}0$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $-1$
7 $[7, 7, w + 1]$ $1$
7 $[7, 7, w + 6]$ $1$