Properties

Base field \(\Q(\sqrt{15}) \)
Weight [2, 2]
Level norm 162
Level $[162, 18, 9w + 9]$
Label 2.2.60.1-162.1-f
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 $[162, 18, 9w + 9]$
Label 2.2.60.1-162.1-f
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 104

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}1$
3 $[3, 3, w]$ $\phantom{-}0$
5 $[5, 5, w]$ $-3$
7 $[7, 7, w + 1]$ $-1$
7 $[7, 7, w + 6]$ $-1$
11 $[11, 11, -w - 2]$ $\phantom{-}3$
11 $[11, 11, w - 2]$ $\phantom{-}3$
17 $[17, 17, w + 7]$ $\phantom{-}0$
17 $[17, 17, w + 10]$ $\phantom{-}0$
43 $[43, 43, w + 12]$ $-10$
43 $[43, 43, w + 31]$ $-10$
53 $[53, 53, w + 11]$ $-9$
53 $[53, 53, w + 42]$ $-9$
59 $[59, 59, 2w - 1]$ $-12$
59 $[59, 59, -2w - 1]$ $-12$
61 $[61, 61, 2w - 11]$ $\phantom{-}8$
61 $[61, 61, -2w - 11]$ $\phantom{-}8$
67 $[67, 67, w + 22]$ $\phantom{-}14$
67 $[67, 67, w + 45]$ $\phantom{-}14$
71 $[71, 71, 3w - 8]$ $\phantom{-}0$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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