Properties

Base field \(\Q(\sqrt{85}) \)
Weight [2, 2]
Level norm 7
Level $[7,7,-w + 1]$
Label 2.2.85.1-7.2-b
Dimension 5
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-b
Dimension 5
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:
\(x^{5} \) \(\mathstrut +\mathstrut 2x^{4} \) \(\mathstrut -\mathstrut 12x^{3} \) \(\mathstrut -\mathstrut 13x^{2} \) \(\mathstrut +\mathstrut 37x \) \(\mathstrut -\mathstrut 16\)

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Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $\phantom{-}e^{3} - 9e + 4$
4 $[4, 2, 2]$ $-e^{4} - 3e^{3} + 10e^{2} + 23e - 23$
5 $[5, 5, w + 2]$ $\phantom{-}2e^{3} - e^{2} - 18e + 14$
7 $[7, 7, w]$ $\phantom{-}e^{4} + e^{3} - 10e^{2} - 6e + 12$
7 $[7, 7, w + 6]$ $\phantom{-}1$
17 $[17, 17, w + 8]$ $-2e^{3} + e^{2} + 18e - 18$
19 $[19, 19, w + 1]$ $-2e^{3} + e^{2} + 17e - 20$
19 $[19, 19, w - 2]$ $\phantom{-}3e^{4} + 6e^{3} - 28e^{2} - 41e + 44$
23 $[23, 23, w + 9]$ $-2e^{3} + 16e - 12$
23 $[23, 23, w + 13]$ $\phantom{-}2e^{4} - 17e^{2} + 8e$
37 $[37, 37, w + 11]$ $-3e^{4} - 8e^{3} + 28e^{2} + 56e - 54$
37 $[37, 37, w + 25]$ $-e^{4} + e^{3} + 9e^{2} - 11e + 2$
59 $[59, 59, 3w + 10]$ $\phantom{-}e^{4} + 4e^{3} - 11e^{2} - 33e + 36$
59 $[59, 59, 3w - 13]$ $\phantom{-}5e^{3} - e^{2} - 42e + 28$
73 $[73, 73, w + 15]$ $\phantom{-}e^{4} - 9e^{2} + 4e - 6$
73 $[73, 73, w + 57]$ $-2e^{3} + e^{2} + 20e - 14$
89 $[89, 89, -w - 10]$ $-5e^{4} - 3e^{3} + 46e^{2} + 10e - 30$
89 $[89, 89, w - 11]$ $-4e^{4} - 9e^{3} + 38e^{2} + 63e - 70$
97 $[97, 97, w + 22]$ $-e^{4} - 2e^{3} + 11e^{2} + 14e - 26$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
7 $[7,7,-w + 1]$ $-1$