Properties

Label 4.4.11324.1-13.1-c
Base field 4.4.11324.1
Weight $[2, 2, 2, 2]$
Level norm $13$
Level $[13, 13, -w^{2} + 3]$
Dimension $2$
CM no
Base change no

Related objects

Downloads

Learn more about

Base field 4.4.11324.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 4x + 2\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[13, 13, -w^{2} + 3]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $19$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} + 2x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}e$
4 $[4, 2, -w^{3} + 4w + 1]$ $-e - 2$
5 $[5, 5, w + 1]$ $\phantom{-}e + 1$
13 $[13, 13, -w^{2} + 3]$ $\phantom{-}1$
17 $[17, 17, -w^{3} + w^{2} + 3w - 1]$ $\phantom{-}e - 3$
19 $[19, 19, -w^{3} + 3w - 1]$ $-e - 3$
23 $[23, 23, -w + 3]$ $\phantom{-}2$
31 $[31, 31, -w^{2} - 2w + 1]$ $\phantom{-}4e + 2$
41 $[41, 41, w^{3} + w^{2} - 5w - 3]$ $-4e - 4$
43 $[43, 43, 2w - 1]$ $-e - 7$
53 $[53, 53, -w - 3]$ $-2e + 8$
53 $[53, 53, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}4e + 2$
61 $[61, 61, w^{3} - 3w - 5]$ $-e + 5$
67 $[67, 67, w^{3} + w^{2} - 5w - 1]$ $-4e + 6$
81 $[81, 3, -3]$ $-2$
83 $[83, 83, -w^{3} + 5w - 3]$ $-e + 1$
89 $[89, 89, w^{2} + 1]$ $\phantom{-}5e + 3$
97 $[97, 97, w^{3} - w^{2} - 5w + 1]$ $-2e - 2$
97 $[97, 97, 3w^{3} - 5w^{2} - 14w + 21]$ $-10e - 12$
97 $[97, 97, w^{3} - 3w - 3]$ $-3e - 9$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, -w^{2} + 3]$ $-1$