Properties

Label 4.4.6224.1-35.1-e
Base field 4.4.6224.1
Weight $[2, 2, 2, 2]$
Level norm $35$
Level $[35, 35, w^{3} - 4w]$
Dimension $2$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 4.4.6224.1

Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 2x + 5\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[35, 35, w^{3} - 4w]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $14$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{2} - 3x - 22\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w^{3} - w^{2} - 4w + 2]$ $\phantom{-}1$
5 $[5, 5, w]$ $\phantom{-}1$
7 $[7, 7, -w^{3} + w^{2} + 3w - 2]$ $\phantom{-}1$
13 $[13, 13, -w^{3} + 4w + 2]$ $\phantom{-}e$
19 $[19, 19, w^{3} - w^{2} - 5w + 2]$ $\phantom{-}e - 2$
29 $[29, 29, -w^{2} - w + 3]$ $\phantom{-}e + 4$
29 $[29, 29, w^{2} - w - 1]$ $\phantom{-}2$
37 $[37, 37, -w^{2} + 2w + 2]$ $\phantom{-}e - 4$
37 $[37, 37, -w^{3} + 5w + 1]$ $\phantom{-}2$
41 $[41, 41, -w^{3} + 2w^{2} + 3w - 7]$ $-e$
47 $[47, 47, w^{3} - 2w^{2} - 4w + 2]$ $-2e + 4$
47 $[47, 47, 2w^{3} - 3w^{2} - 8w + 6]$ $\phantom{-}e - 2$
59 $[59, 59, -2w^{3} + w^{2} + 7w - 3]$ $\phantom{-}8$
67 $[67, 67, w^{3} - 2w^{2} - 3w + 1]$ $-e - 6$
73 $[73, 73, -2w - 1]$ $\phantom{-}2e + 2$
79 $[79, 79, 2w^{2} - 2w - 9]$ $\phantom{-}8$
81 $[81, 3, -3]$ $\phantom{-}2$
97 $[97, 97, -3w + 2]$ $-2e + 2$
101 $[101, 101, w^{3} - 3w^{2} - w + 4]$ $\phantom{-}e + 8$
101 $[101, 101, 2w^{3} - w^{2} - 9w + 1]$ $-6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, w]$ $-1$
$7$ $[7, 7, -w^{3} + w^{2} + 3w - 2]$ $-1$