Properties

Base field \(\Q(\sqrt{3}) \)
Weight [2, 2]
Level norm 59
Level $[59,59,-5w - 4]$
Label 2.2.12.1-59.2-a
Dimension 2
CM no
Base change no

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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 $[59,59,-5w - 4]$
Label 2.2.12.1-59.2-a
Dimension 2
Is CM no
Is base change no
Parent newspace dimension 4

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} \) \(\mathstrut -\mathstrut x \) \(\mathstrut -\mathstrut 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}e$
3 $[3, 3, w]$ $-e + 2$
11 $[11, 11, -2w + 1]$ $\phantom{-}2e + 1$
11 $[11, 11, 2w + 1]$ $\phantom{-}e + 4$
13 $[13, 13, w + 4]$ $\phantom{-}4e - 3$
13 $[13, 13, -w + 4]$ $-3e - 2$
23 $[23, 23, -3w + 2]$ $-4e + 1$
23 $[23, 23, 3w + 2]$ $-3e + 3$
25 $[25, 5, 5]$ $\phantom{-}2e - 5$
37 $[37, 37, 2w - 7]$ $\phantom{-}3e - 6$
37 $[37, 37, -2w - 7]$ $-6e + 1$
47 $[47, 47, -4w - 1]$ $\phantom{-}7e - 3$
47 $[47, 47, 4w - 1]$ $\phantom{-}4e - 9$
49 $[49, 7, -7]$ $\phantom{-}e + 2$
59 $[59, 59, 5w - 4]$ $-4e - 3$
59 $[59, 59, -5w - 4]$ $-1$
61 $[61, 61, -w - 8]$ $-e$
61 $[61, 61, w - 8]$ $\phantom{-}6e - 6$
71 $[71, 71, 5w - 2]$ $\phantom{-}10e - 8$
71 $[71, 71, -5w - 2]$ $-5e + 12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
59 $[59,59,-5w - 4]$ $1$