Properties

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

Related objects

Downloads

Learn more about

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 $[4, 2, 2]$
Label 2.2.85.1-4.1-e
Dimension 4
Is CM no
Is base change no
Parent newspace dimension 10

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} \) \(\mathstrut +\mathstrut 9x^{2} \) \(\mathstrut +\mathstrut 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $-e$
4 $[4, 2, 2]$ $-1$
5 $[5, 5, w + 2]$ $\phantom{-}0$
7 $[7, 7, w]$ $\phantom{-}e^{3} + 9e$
7 $[7, 7, w + 6]$ $-e^{3} - 9e$
17 $[17, 17, w + 8]$ $\phantom{-}0$
19 $[19, 19, w + 1]$ $-e^{2} - 2$
19 $[19, 19, w - 2]$ $-e^{2} - 2$
23 $[23, 23, w + 9]$ $\phantom{-}e^{3} + 7e$
23 $[23, 23, w + 13]$ $-e^{3} - 7e$
37 $[37, 37, w + 11]$ $-2e^{3} - 16e$
37 $[37, 37, w + 25]$ $\phantom{-}2e^{3} + 16e$
59 $[59, 59, 3w + 10]$ $\phantom{-}e^{2} + 10$
59 $[59, 59, 3w - 13]$ $\phantom{-}e^{2} + 10$
73 $[73, 73, w + 15]$ $\phantom{-}e^{3} + 14e$
73 $[73, 73, w + 57]$ $-e^{3} - 14e$
89 $[89, 89, -w - 10]$ $\phantom{-}e^{2} - 2$
89 $[89, 89, w - 11]$ $\phantom{-}e^{2} - 2$
97 $[97, 97, w + 22]$ $\phantom{-}3e^{3} + 26e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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