Properties

Base field \(\Q(\sqrt{85}) \)
Weight [2, 2]
Level norm 12
Level $[12, 6, 2w]$
Label 2.2.85.1-12.1-e
Dimension 4
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 $[12, 6, 2w]$
Label 2.2.85.1-12.1-e
Dimension 4
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:
\(x^{4} \) \(\mathstrut +\mathstrut 12x^{2} \) \(\mathstrut +\mathstrut 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $-\frac{1}{8}e^{3} - e$
3 $[3, 3, w + 2]$ $\phantom{-}0$
4 $[4, 2, 2]$ $\phantom{-}1$
5 $[5, 5, w + 2]$ $\phantom{-}e$
7 $[7, 7, w]$ $-\frac{1}{2}e^{3} - 5e$
7 $[7, 7, w + 6]$ $-e$
17 $[17, 17, w + 8]$ $-\frac{1}{2}e^{3} - 4e$
19 $[19, 19, w + 1]$ $\phantom{-}e^{2} + 4$
19 $[19, 19, w - 2]$ $-e^{2} - 4$
23 $[23, 23, w + 9]$ $\phantom{-}\frac{1}{2}e^{3} + 5e$
23 $[23, 23, w + 13]$ $\phantom{-}e$
37 $[37, 37, w + 11]$ $-\frac{1}{2}e^{3} - 5e$
37 $[37, 37, w + 25]$ $\phantom{-}\frac{1}{2}e^{3} + 7e$
59 $[59, 59, 3w + 10]$ $-4$
59 $[59, 59, 3w - 13]$ $\phantom{-}2e^{2} + 12$
73 $[73, 73, w + 15]$ $-e^{3} - 14e$
73 $[73, 73, w + 57]$ $-e^{3} - 10e$
89 $[89, 89, -w - 10]$ $-e^{2} - 18$
89 $[89, 89, w - 11]$ $-e^{2} - 2$
97 $[97, 97, w + 22]$ $\phantom{-}\frac{3}{2}e^{3} + 12e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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