Properties

Base field \(\Q(\sqrt{85}) \)
Weight [2, 2]
Level norm 9
Level $[9, 3, 3]$
Label 2.2.85.1-9.1-c
Dimension 4
CM no
Base change yes

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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 $[9, 3, 3]$
Label 2.2.85.1-9.1-c
Dimension 4
Is CM no
Is base change yes
Parent newspace dimension 18

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} \) \(\mathstrut -\mathstrut 6x^{3} \) \(\mathstrut +\mathstrut 6x^{2} \) \(\mathstrut +\mathstrut 11x \) \(\mathstrut -\mathstrut 8\)

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

Atkin-Lehner eigenvalues

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