Properties

Base field 3.3.940.1
Weight [2, 2, 2]
Level norm 5
Level $[5, 5, -w^{2} + w + 5]$
Label 3.3.940.1-5.2-c
Dimension 4
CM no
Base change no

Related objects

Downloads

Learn more about

Base field 3.3.940.1

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

Form

Weight [2, 2, 2]
Level $[5, 5, -w^{2} + w + 5]$
Label 3.3.940.1-5.2-c
Dimension 4
Is CM no
Is base change no
Parent newspace dimension 7

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - x^{3} - 6x^{2} + 7x + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $\phantom{-}e$
2 $[2, 2, -w - 1]$ $\phantom{-}e^{3} - 5e + 2$
5 $[5, 5, -w^{2} + w + 7]$ $\phantom{-}e^{2} - 3$
5 $[5, 5, -w^{2} + w + 5]$ $\phantom{-}1$
17 $[17, 17, -w^{2} + 3w + 1]$ $-e^{2} + 5$
23 $[23, 23, -w^{2} + w + 3]$ $-2e^{3} + e^{2} + 10e - 5$
27 $[27, 3, 3]$ $\phantom{-}e^{3} - e^{2} - 7e + 9$
29 $[29, 29, -w^{2} + 3w - 1]$ $\phantom{-}e^{3} + 2e^{2} - 3e - 6$
37 $[37, 37, w^{2} + w + 1]$ $-e^{3} - e^{2} + 3e - 1$
41 $[41, 41, w^{2} - w - 9]$ $\phantom{-}e^{3} - 2e^{2} - 7e + 10$
43 $[43, 43, -3w^{2} + 3w + 17]$ $-2e^{3} + 12e - 4$
47 $[47, 47, 2w^{2} - 2w - 13]$ $-e^{2} + 13$
47 $[47, 47, -2w + 5]$ $\phantom{-}e^{3} + e^{2} - 5e + 5$
53 $[53, 53, 3w^{2} - w - 19]$ $\phantom{-}2e^{2} - 8$
59 $[59, 59, 2w - 1]$ $-e^{3} - e^{2} + 3e - 1$
67 $[67, 67, w^{2} + w - 5]$ $-4e^{3} - 4e^{2} + 16e + 10$
71 $[71, 71, -3w^{2} + w + 21]$ $\phantom{-}e^{2} - 3$
79 $[79, 79, 3w^{2} - w - 23]$ $-e^{3} + e^{2} + 3e + 1$
89 $[89, 89, 2w^{2} - 4w - 7]$ $-5e^{3} - 3e^{2} + 27e - 5$
89 $[89, 89, -2w^{2} - 2w + 5]$ $-e^{2} + 4e - 1$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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