Properties

Base field 3.3.940.1
Weight [2, 2, 2]
Level norm 10
Level $[10, 10, w - 1]$
Label 3.3.940.1-10.4-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 $[10, 10, w - 1]$
Label 3.3.940.1-10.4-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:
\(x^{4} - 8x^{2} - x + 10\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $\phantom{-}e$
2 $[2, 2, -w - 1]$ $-1$
5 $[5, 5, -w^{2} + w + 7]$ $-e^{2} + e + 4$
5 $[5, 5, -w^{2} + w + 5]$ $\phantom{-}1$
17 $[17, 17, -w^{2} + 3w + 1]$ $\phantom{-}e^{3} - 6e + 1$
23 $[23, 23, -w^{2} + w + 3]$ $\phantom{-}e^{2} - e - 6$
27 $[27, 3, 3]$ $\phantom{-}e^{2} + e$
29 $[29, 29, -w^{2} + 3w - 1]$ $-e^{3} + e^{2} + 5e + 1$
37 $[37, 37, w^{2} + w + 1]$ $-e^{3} + 2e^{2} + 6e - 3$
41 $[41, 41, w^{2} - w - 9]$ $-e^{3} - 2e^{2} + 4e + 11$
43 $[43, 43, -3w^{2} + 3w + 17]$ $-e^{3} + 2e^{2} + 2e - 9$
47 $[47, 47, 2w^{2} - 2w - 13]$ $-e^{3} + 4e - 1$
47 $[47, 47, -2w + 5]$ $\phantom{-}e^{3} - 2e^{2} - 8e + 7$
53 $[53, 53, 3w^{2} - w - 19]$ $\phantom{-}e^{2} - 3e - 2$
59 $[59, 59, 2w - 1]$ $-3e^{2} + 3e + 14$
67 $[67, 67, w^{2} + w - 5]$ $\phantom{-}e^{2} + 3e - 6$
71 $[71, 71, -3w^{2} + w + 21]$ $\phantom{-}e^{3} - 3e^{2} - 7e + 13$
79 $[79, 79, 3w^{2} - w - 23]$ $-e^{3} - e^{2} + 11e + 3$
89 $[89, 89, 2w^{2} - 4w - 7]$ $\phantom{-}e^{3} - e^{2} - 5e + 7$
89 $[89, 89, -2w^{2} - 2w + 5]$ $\phantom{-}2e^{3} + 2e^{2} - 12e - 10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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