Properties

Label 2.2.85.1-4.1-b
Base field \(\Q(\sqrt{85}) \)
Weight $[2, 2]$
Level norm $4$
Level $[4, 2, 2]$
Dimension $1$
CM no
Base change yes

Related objects

Downloads

Learn more

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: $[4, 2, 2]$
Dimension: $1$
CM: no
Base change: yes
Newspace dimension: $10$

Hecke eigenvalues ($q$-expansion)

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

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, 2]$ $1$