Properties

Label 2.2.60.1-9.1-b
Base field \(\Q(\sqrt{15}) \)
Weight $[2, 2]$
Level norm $9$
Level $[9, 3, 3]$
Dimension $2$
CM yes
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: $[9, 3, 3]$
Dimension: $2$
CM: yes
Base change: yes
Newspace dimension: $16$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{2} + 5\)

  Show full eigenvalues   Hide large eigenvalues

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

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w]$ $1$