Properties

Label 2.2.85.1-3.2-b
Base field \(\Q(\sqrt{85}) \)
Weight $[2, 2]$
Level norm $3$
Level $[3,3,-w + 1]$
Dimension $1$
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: $[3,3,-w + 1]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $2$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w]$ $-2$
3 $[3, 3, w + 2]$ $\phantom{-}1$
4 $[4, 2, 2]$ $-1$
5 $[5, 5, w + 2]$ $\phantom{-}0$
7 $[7, 7, w]$ $\phantom{-}2$
7 $[7, 7, w + 6]$ $-4$
17 $[17, 17, w + 8]$ $-6$
19 $[19, 19, w + 1]$ $-4$
19 $[19, 19, w - 2]$ $\phantom{-}8$
23 $[23, 23, w + 9]$ $-6$
23 $[23, 23, w + 13]$ $\phantom{-}0$
37 $[37, 37, w + 11]$ $-10$
37 $[37, 37, w + 25]$ $\phantom{-}2$
59 $[59, 59, 3w + 10]$ $-12$
59 $[59, 59, 3w - 13]$ $\phantom{-}0$
73 $[73, 73, w + 15]$ $\phantom{-}8$
73 $[73, 73, w + 57]$ $\phantom{-}8$
89 $[89, 89, -w - 10]$ $-6$
89 $[89, 89, w - 11]$ $\phantom{-}6$
97 $[97, 97, w + 22]$ $-10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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