Properties

Label 2.2.60.1-30.1-d
Base field \(\Q(\sqrt{15}) \)
Weight $[2, 2]$
Level norm $30$
Level $[30, 30, w + 15]$
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: $[30, 30, w + 15]$
Dimension: $1$
CM: no
Base change: yes
Newspace dimension: $20$

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 $[5, 5, w]$ $\phantom{-}1$
7 $[7, 7, w + 1]$ $-4$
7 $[7, 7, w + 6]$ $-4$
11 $[11, 11, -w - 2]$ $\phantom{-}0$
11 $[11, 11, w - 2]$ $\phantom{-}0$
17 $[17, 17, w + 7]$ $-6$
17 $[17, 17, w + 10]$ $-6$
43 $[43, 43, w + 12]$ $-4$
43 $[43, 43, w + 31]$ $-4$
53 $[53, 53, w + 11]$ $\phantom{-}6$
53 $[53, 53, w + 42]$ $\phantom{-}6$
59 $[59, 59, 2w - 1]$ $\phantom{-}0$
59 $[59, 59, -2w - 1]$ $\phantom{-}0$
61 $[61, 61, 2w - 11]$ $-10$
61 $[61, 61, -2w - 11]$ $-10$
67 $[67, 67, w + 22]$ $-4$
67 $[67, 67, w + 45]$ $-4$
71 $[71, 71, 3w - 8]$ $\phantom{-}0$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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