Properties

Base field \(\Q(\sqrt{67}) \)
Weight [2, 2]
Level norm 9
Level $[9, 9, 16w + 131]$
Label 2.2.268.1-9.2-f
Dimension 4
CM no
Base change no

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Base field \(\Q(\sqrt{67}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 67\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2]
Level $[9, 9, 16w + 131]$
Label 2.2.268.1-9.2-f
Dimension 4
Is CM no
Is base change no
Parent newspace dimension 48

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} \) \(\mathstrut -\mathstrut 9x^{2} \) \(\mathstrut +\mathstrut 19\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -27w + 221]$ $\phantom{-}e$
3 $[3, 3, -w + 8]$ $-e^{3} + 5e$
3 $[3, 3, -w - 8]$ $\phantom{-}0$
7 $[7, 7, -11w + 90]$ $\phantom{-}e$
7 $[7, 7, -11w - 90]$ $-e$
11 $[11, 11, 6w - 49]$ $\phantom{-}e^{3} - 6e$
11 $[11, 11, 6w + 49]$ $\phantom{-}e^{3} - 6e$
17 $[17, 17, 4w + 33]$ $-4e^{2} + 18$
17 $[17, 17, -4w + 33]$ $\phantom{-}4e^{2} - 18$
25 $[25, 5, -5]$ $\phantom{-}6e^{2} - 29$
29 $[29, 29, -70w + 573]$ $\phantom{-}2e^{2} - 7$
29 $[29, 29, 151w - 1236]$ $-2e^{2} + 7$
31 $[31, 31, -w - 6]$ $-e^{3} + 8e$
31 $[31, 31, w - 6]$ $\phantom{-}e^{3} - 8e$
37 $[37, 37, -21w - 172]$ $-3e^{2} + 9$
37 $[37, 37, -21w + 172]$ $-3e^{2} + 9$
43 $[43, 43, 2w - 15]$ $-e^{3} + 5e$
43 $[43, 43, 2w + 15]$ $\phantom{-}e^{3} - 5e$
67 $[67, 67, -w]$ $\phantom{-}0$
73 $[73, 73, -3w - 26]$ $\phantom{-}2e^{2} - 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w - 8]$ $-1$