Properties

Base field \(\Q(\sqrt{3}) \)
Weight [2, 2]
Level norm 69
Level $[69, 69, 2w - 9]$
Label 2.2.12.1-69.1-a
Dimension 3
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 $[69, 69, 2w - 9]$
Label 2.2.12.1-69.1-a
Dimension 3
Is CM no
Is base change no
Parent newspace dimension 6

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} \) \(\mathstrut -\mathstrut x^{2} \) \(\mathstrut -\mathstrut 4x \) \(\mathstrut +\mathstrut 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}e$
3 $[3, 3, w]$ $-1$
11 $[11, 11, -2w + 1]$ $-2e^{2} + 6$
11 $[11, 11, 2w + 1]$ $\phantom{-}e^{2} - e - 2$
13 $[13, 13, w + 4]$ $-e^{2} + e + 4$
13 $[13, 13, -w + 4]$ $-e^{2} + e + 4$
23 $[23, 23, -3w + 2]$ $-1$
23 $[23, 23, 3w + 2]$ $\phantom{-}2e^{2} - 2e - 4$
25 $[25, 5, 5]$ $-e^{2} - 3e + 4$
37 $[37, 37, 2w - 7]$ $\phantom{-}4e^{2} - 4e - 10$
37 $[37, 37, -2w - 7]$ $\phantom{-}2e$
47 $[47, 47, -4w - 1]$ $-3e^{2} + 3e + 10$
47 $[47, 47, 4w - 1]$ $-2e^{2} - 2e + 8$
49 $[49, 7, -7]$ $\phantom{-}2e^{2} + 2e - 6$
59 $[59, 59, 5w - 4]$ $-e^{2} - 3e + 6$
59 $[59, 59, -5w - 4]$ $\phantom{-}4e^{2} - 8$
61 $[61, 61, -w - 8]$ $-6e$
61 $[61, 61, w - 8]$ $\phantom{-}2e^{2} - 2e - 6$
71 $[71, 71, 5w - 2]$ $\phantom{-}2e^{2} - 4e - 14$
71 $[71, 71, -5w - 2]$ $-2e^{2} + 6e + 8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $1$
23 $[23, 23, -3w + 2]$ $1$