Properties

Base field \(\Q(\sqrt{85}) \)
Weight [2, 2]
Level norm 12
Level $[12,6,-2w + 2]$
Label 2.2.85.1-12.2-c
Dimension 3
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-c
Dimension 3
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:
\(x^{3} \) \(\mathstrut -\mathstrut 8x \) \(\mathstrut +\mathstrut 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $\phantom{-}1$
4 $[4, 2, 2]$ $\phantom{-}1$
5 $[5, 5, w + 2]$ $\phantom{-}\frac{1}{2}e^{2} - 2$
7 $[7, 7, w]$ $-\frac{1}{2}e^{2} - e + 2$
7 $[7, 7, w + 6]$ $\phantom{-}\frac{1}{2}e^{2}$
17 $[17, 17, w + 8]$ $-e + 4$
19 $[19, 19, w + 1]$ $\phantom{-}e - 2$
19 $[19, 19, w - 2]$ $-e^{2} - e + 4$
23 $[23, 23, w + 9]$ $-\frac{3}{2}e^{2} + e + 8$
23 $[23, 23, w + 13]$ $-\frac{1}{2}e^{2} - 2e + 4$
37 $[37, 37, w + 11]$ $\phantom{-}\frac{1}{2}e^{2} - e - 2$
37 $[37, 37, w + 25]$ $-\frac{3}{2}e^{2} - e + 12$
59 $[59, 59, 3w + 10]$ $-e^{2} + 4$
59 $[59, 59, 3w - 13]$ $\phantom{-}e^{2} + 4e - 8$
73 $[73, 73, w + 15]$ $\phantom{-}4e + 4$
73 $[73, 73, w + 57]$ $\phantom{-}e^{2} + 2e - 4$
89 $[89, 89, -w - 10]$ $-2e^{2} - 3e + 8$
89 $[89, 89, w - 11]$ $-2e^{2} - 5e + 16$
97 $[97, 97, w + 22]$ $-e^{2} - 3e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3,3,-w + 1]$ $-1$
4 $[4,2,2]$ $-1$