Properties

Label 2.2.12.1-600.1-c
Base field \(\Q(\sqrt{3}) \)
Weight $[2, 2]$
Level norm $600$
Level $[600, 60, 10w - 30]$
Dimension $1$
CM no
Base change yes

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Base field \(\Q(\sqrt{3}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 3\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[600, 60, 10w - 30]$
Dimension: $1$
CM: no
Base change: yes
Newspace dimension: $12$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}0$
3 $[3, 3, w]$ $\phantom{-}1$
11 $[11, 11, -2w + 1]$ $-4$
11 $[11, 11, 2w + 1]$ $-4$
13 $[13, 13, w + 4]$ $\phantom{-}6$
13 $[13, 13, -w + 4]$ $\phantom{-}6$
23 $[23, 23, -3w + 2]$ $\phantom{-}0$
23 $[23, 23, 3w + 2]$ $\phantom{-}0$
25 $[25, 5, 5]$ $\phantom{-}1$
37 $[37, 37, 2w - 7]$ $-2$
37 $[37, 37, -2w - 7]$ $-2$
47 $[47, 47, -4w - 1]$ $\phantom{-}8$
47 $[47, 47, 4w - 1]$ $\phantom{-}8$
49 $[49, 7, -7]$ $-14$
59 $[59, 59, 5w - 4]$ $\phantom{-}12$
59 $[59, 59, -5w - 4]$ $\phantom{-}12$
61 $[61, 61, -w - 8]$ $\phantom{-}14$
61 $[61, 61, w - 8]$ $\phantom{-}14$
71 $[71, 71, 5w - 2]$ $\phantom{-}8$
71 $[71, 71, -5w - 2]$ $\phantom{-}8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w + 1]$ $1$
$3$ $[3, 3, w]$ $-1$
$25$ $[25, 5, 5]$ $-1$