Properties

Base field \(\Q(\sqrt{85}) \)
Weight [2, 2]
Level norm 12
Level $[12,6,-2w + 2]$
Label 2.2.85.1-12.2-f
Dimension 6
CM no
Base change no

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Base field \(\Q(\sqrt{85}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 21\); narrow class number \(2\) and class number \(2\).

Form

Weight [2, 2]
Level $[12,6,-2w + 2]$
Label 2.2.85.1-12.2-f
Dimension 6
Is CM no
Is base change no
Parent newspace dimension 18

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} \) \(\mathstrut +\mathstrut 12x^{4} \) \(\mathstrut +\mathstrut 32x^{2} \) \(\mathstrut +\mathstrut 16\)

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Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $\phantom{-}\frac{1}{8}e^{5} + \frac{5}{4}e^{3} + 2e$
4 $[4, 2, 2]$ $-1$
5 $[5, 5, w + 2]$ $-\frac{3}{8}e^{5} - 4e^{3} - 6e$
7 $[7, 7, w]$ $-\frac{1}{8}e^{5} - 2e^{3} - 7e$
7 $[7, 7, w + 6]$ $-\frac{1}{8}e^{5} - \frac{3}{2}e^{3} - 4e$
17 $[17, 17, w + 8]$ $-\frac{1}{2}e^{5} - 5e^{3} - 9e$
19 $[19, 19, w + 1]$ $\phantom{-}\frac{3}{4}e^{4} + 7e^{2} + 10$
19 $[19, 19, w - 2]$ $-\frac{3}{4}e^{4} - 6e^{2} - 4$
23 $[23, 23, w + 9]$ $-\frac{1}{8}e^{5} - \frac{3}{2}e^{3} - e$
23 $[23, 23, w + 13]$ $\phantom{-}\frac{5}{8}e^{5} + \frac{13}{2}e^{3} + 10e$
37 $[37, 37, w + 11]$ $-\frac{9}{8}e^{5} - 12e^{3} - 21e$
37 $[37, 37, w + 25]$ $\phantom{-}\frac{1}{8}e^{5} + \frac{5}{2}e^{3} + 11e$
59 $[59, 59, 3w + 10]$ $-e^{4} - 9e^{2} - 8$
59 $[59, 59, 3w - 13]$ $-e^{4} - 9e^{2} - 8$
73 $[73, 73, w + 15]$ $\phantom{-}\frac{1}{2}e^{5} + 7e^{3} + 20e$
73 $[73, 73, w + 57]$ $-\frac{3}{4}e^{5} - 8e^{3} - 10e$
89 $[89, 89, -w - 10]$ $\phantom{-}\frac{1}{4}e^{4} + 3e^{2} + 4$
89 $[89, 89, w - 11]$ $\phantom{-}\frac{1}{4}e^{4} + 3e^{2} + 4$
97 $[97, 97, w + 22]$ $\phantom{-}\frac{3}{4}e^{5} + 9e^{3} + 25e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3,3,-w + 1]$ $-\frac{1}{8}e^{5} - \frac{5}{4}e^{3} - 2e$
4 $[4,2,2]$ $1$