Properties

Base field \(\Q(\sqrt{85}) \)
Weight [2, 2]
Level norm 7
Level $[7,7,-w + 1]$
Label 2.2.85.1-7.2-c
Dimension 8
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 $[7,7,-w + 1]$
Label 2.2.85.1-7.2-c
Dimension 8
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:
\(x^{8} \) \(\mathstrut +\mathstrut 12x^{6} \) \(\mathstrut +\mathstrut 38x^{4} \) \(\mathstrut +\mathstrut 13x^{2} \) \(\mathstrut +\mathstrut 1\)

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Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $-e^{3} - 5e$
4 $[4, 2, 2]$ $\phantom{-}e^{6} + 12e^{4} + 37e^{2} + 6$
5 $[5, 5, w + 2]$ $-4e^{7} - 47e^{5} - 142e^{3} - 27e$
7 $[7, 7, w]$ $-e^{7} - 12e^{5} - 36e^{3} - 2e$
7 $[7, 7, w + 6]$ $\phantom{-}e^{7} + 12e^{5} + 37e^{3} + 7e$
17 $[17, 17, w + 8]$ $\phantom{-}4e^{7} + 47e^{5} + 142e^{3} + 27e$
19 $[19, 19, w + 1]$ $-e^{4} - 7e^{2} - 1$
19 $[19, 19, w - 2]$ $-2e^{4} - 12e^{2} - 5$
23 $[23, 23, w + 9]$ $-4e^{7} - 48e^{5} - 150e^{3} - 40e$
23 $[23, 23, w + 13]$ $\phantom{-}e^{5} + 8e^{3} + 13e$
37 $[37, 37, w + 11]$ $-3e^{7} - 34e^{5} - 97e^{3} - 8e$
37 $[37, 37, w + 25]$ $-5e^{7} - 59e^{5} - 178e^{3} - 26e$
59 $[59, 59, 3w + 10]$ $\phantom{-}2e^{6} + 28e^{4} + 97e^{2} + 11$
59 $[59, 59, 3w - 13]$ $\phantom{-}e^{6} + 12e^{4} + 38e^{2} + 12$
73 $[73, 73, w + 15]$ $\phantom{-}9e^{7} + 107e^{5} + 327e^{3} + 65e$
73 $[73, 73, w + 57]$ $-e^{5} - 2e^{3} + 25e$
89 $[89, 89, -w - 10]$ $\phantom{-}3e^{6} + 31e^{4} + 79e^{2} + 6$
89 $[89, 89, w - 11]$ $\phantom{-}5e^{6} + 59e^{4} + 177e^{2} + 33$
97 $[97, 97, w + 22]$ $-3e^{7} - 35e^{5} - 103e^{3} - 3e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
7 $[7,7,-w + 1]$ $-e^{7} - 12e^{5} - 37e^{3} - 7e$