Properties

Base field \(\Q(\sqrt{34}) \)
Weight [2, 2]
Level norm 6
Level $[6,6,-w + 2]$
Label 2.2.136.1-6.2-f
Dimension 6
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-f
Dimension 6
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:
\(x^{6} \) \(\mathstrut +\mathstrut 8x^{4} \) \(\mathstrut +\mathstrut 16x^{2} \) \(\mathstrut +\mathstrut 4\)

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Norm Prime Eigenvalue
2 $[2, 2, w - 6]$ $\phantom{-}1$
3 $[3, 3, w + 1]$ $\phantom{-}\frac{1}{2}e^{3} + 2e$
3 $[3, 3, w + 2]$ $\phantom{-}e$
5 $[5, 5, w + 2]$ $\phantom{-}\frac{1}{2}e^{5} + 3e^{3} + 2e$
5 $[5, 5, w + 3]$ $\phantom{-}e^{3} + 3e$
11 $[11, 11, w + 1]$ $-\frac{1}{2}e^{5} - 2e^{3} + e$
11 $[11, 11, w + 10]$ $-\frac{3}{2}e^{5} - 9e^{3} - 10e$
17 $[17, 17, -3w + 17]$ $-2e^{2} - 4$
29 $[29, 29, w + 11]$ $\phantom{-}4e$
29 $[29, 29, w + 18]$ $\phantom{-}\frac{3}{2}e^{5} + 9e^{3} + 9e$
37 $[37, 37, w + 16]$ $-2e$
37 $[37, 37, w + 21]$ $\phantom{-}\frac{5}{2}e^{5} + 17e^{3} + 25e$
47 $[47, 47, -w - 9]$ $-e^{4} - 5e^{2} - 6$
47 $[47, 47, w - 9]$ $\phantom{-}3e^{4} + 17e^{2} + 12$
49 $[49, 7, -7]$ $-e^{4} - 5e^{2} - 4$
61 $[61, 61, w + 20]$ $\phantom{-}4e^{3} + 14e$
61 $[61, 61, w + 41]$ $-\frac{1}{2}e^{5} - 4e^{3} - e$
89 $[89, 89, 2w - 15]$ $-e^{4} - 8e^{2} - 12$
89 $[89, 89, -2w - 15]$ $-e^{4} - 8e^{2} - 12$
103 $[103, 103, -14w + 81]$ $-e^{4} - 4e^{2} - 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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