Properties

Label 2.2.120.1-13.1-b
Base field \(\Q(\sqrt{30}) \)
Weight $[2, 2]$
Level norm $13$
Level $[13, 13, w + 2]$
Dimension $2$
CM no
Base change no

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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: $[13, 13, w + 2]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $60$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} + 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}e$
3 $[3, 3, w]$ $\phantom{-}0$
5 $[5, 5, -w + 5]$ $\phantom{-}2$
7 $[7, 7, w + 3]$ $-e$
7 $[7, 7, w + 4]$ $-e$
13 $[13, 13, w + 2]$ $-\frac{1}{2}e$
13 $[13, 13, w + 11]$ $-e$
17 $[17, 17, w + 8]$ $\phantom{-}3e$
17 $[17, 17, w + 9]$ $\phantom{-}e$
19 $[19, 19, w + 7]$ $-2$
19 $[19, 19, -w + 7]$ $\phantom{-}2$
29 $[29, 29, -w - 1]$ $\phantom{-}10$
29 $[29, 29, w - 1]$ $\phantom{-}2$
37 $[37, 37, w + 17]$ $\phantom{-}e$
37 $[37, 37, w + 20]$ $\phantom{-}3e$
71 $[71, 71, 2w - 7]$ $-8$
71 $[71, 71, -2w - 7]$ $\phantom{-}4$
83 $[83, 83, w + 14]$ $-8e$
83 $[83, 83, w + 69]$ $\phantom{-}2e$
101 $[101, 101, -7w + 37]$ $\phantom{-}14$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, w + 2]$ $\frac{1}{2}e$