Properties

Label 4.4.13676.1-4.2-a
Base field 4.4.13676.1
Weight $[2, 2, 2, 2]$
Level norm $4$
Level $[4, 2, -w^{2} - w + 3]$
Dimension $4$
CM no
Base change no

Related objects

Downloads

Learn more about

Base field 4.4.13676.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + 7x + 1\); narrow class number \(1\) and class number \(1\).

Form

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

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - x^{3} - 6x^{2} + 3x + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}e$
4 $[4, 2, -w^{2} - w + 3]$ $-1$
5 $[5, 5, w^{3} - 5w + 1]$ $\phantom{-}e^{3} - e^{2} - 5e + 3$
11 $[11, 11, -w^{3} + 6w - 2]$ $-e^{3} + 6e + 1$
13 $[13, 13, -w^{2} + 4]$ $\phantom{-}e^{3} - e^{2} - 5e + 1$
17 $[17, 17, 2w^{3} + w^{2} - 10w - 2]$ $-e^{2} + e + 4$
37 $[37, 37, w^{3} + w^{2} - 6w - 3]$ $\phantom{-}e^{3} - e^{2} - 7e + 1$
37 $[37, 37, -w^{3} + 6w - 4]$ $-e^{3} + e^{2} + 7e - 5$
41 $[41, 41, -w^{3} + 5w - 5]$ $-2e^{3} + e^{2} + 13e - 2$
43 $[43, 43, w^{3} - 4w + 4]$ $\phantom{-}2e^{3} - 2e^{2} - 8e + 2$
43 $[43, 43, -2w^{3} + 11w - 2]$ $-3e^{3} + 2e^{2} + 18e - 7$
47 $[47, 47, -2w^{3} - w^{2} + 12w]$ $-2$
47 $[47, 47, 2w - 1]$ $-2e + 4$
61 $[61, 61, -w^{3} + w^{2} + 6w - 5]$ $-2e^{3} + 2e^{2} + 10e - 2$
71 $[71, 71, w^{3} + w^{2} - 4w - 3]$ $\phantom{-}4e^{3} - 4e^{2} - 26e + 8$
71 $[71, 71, 2w^{3} + 2w^{2} - 9w - 2]$ $-2e - 2$
79 $[79, 79, w^{3} + w^{2} - 6w - 5]$ $\phantom{-}2e^{3} - 2e^{2} - 12e$
81 $[81, 3, -3]$ $-3e^{3} + e^{2} + 17e + 3$
83 $[83, 83, -3w^{3} - w^{2} + 16w + 3]$ $\phantom{-}4e + 2$
97 $[97, 97, w^{3} + w^{2} - 6w + 1]$ $\phantom{-}2e^{3} - 3e^{2} - 15e + 6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, -w^{2} - w + 3]$ $1$