Properties

Base field \(\Q(\sqrt{34}) \)
Weight [2, 2]
Level norm 6
Level $[6,6,-w + 2]$
Label 2.2.136.1-6.2-e
Dimension 4
CM no
Base change no

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Base field \(\Q(\sqrt{34}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 34\); narrow class number \(4\) and class number \(2\).

Form

Weight [2, 2]
Level $[6,6,-w + 2]$
Label 2.2.136.1-6.2-e
Dimension 4
Is CM no
Is base change no
Parent newspace dimension 20

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} \) \(\mathstrut +\mathstrut 12x^{2} \) \(\mathstrut +\mathstrut 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w - 6]$ $-1$
3 $[3, 3, w + 1]$ $-\frac{1}{8}e^{3} - e$
3 $[3, 3, w + 2]$ $\phantom{-}e$
5 $[5, 5, w + 2]$ $\phantom{-}0$
5 $[5, 5, w + 3]$ $\phantom{-}e$
11 $[11, 11, w + 1]$ $\phantom{-}\frac{1}{2}e^{3} + 5e$
11 $[11, 11, w + 10]$ $\phantom{-}2e$
17 $[17, 17, -3w + 17]$ $\phantom{-}2$
29 $[29, 29, w + 11]$ $-\frac{1}{2}e^{3} - 4e$
29 $[29, 29, w + 18]$ $-\frac{1}{2}e^{3} - 3e$
37 $[37, 37, w + 16]$ $-\frac{1}{2}e^{3} - 6e$
37 $[37, 37, w + 21]$ $\phantom{-}\frac{1}{2}e^{3} + 5e$
47 $[47, 47, -w - 9]$ $\phantom{-}e^{2} + 8$
47 $[47, 47, w - 9]$ $-e^{2}$
49 $[49, 7, -7]$ $-e^{2} - 10$
61 $[61, 61, w + 20]$ $\phantom{-}\frac{3}{2}e^{3} + 12e$
61 $[61, 61, w + 41]$ $-\frac{1}{2}e^{3} - 3e$
89 $[89, 89, 2w - 15]$ $\phantom{-}2e^{2} + 14$
89 $[89, 89, -2w - 15]$ $-2$
103 $[103, 103, -14w + 81]$ $-2e^{2} - 16$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2,2,-w - 6]$ $1$
3 $[3,3,-w + 2]$ $\frac{1}{8}e^{3} + e$