Properties

Base field 3.3.940.1
Weight [2, 2, 2]
Level norm 4
Level $[4, 4, w]$
Label 3.3.940.1-4.3-a
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 $[4, 4, w]$
Label 3.3.940.1-4.3-a
Dimension 4
Is CM no
Is base change no
Parent newspace dimension 4

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 8x^{2} + 2x + 8\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $\phantom{-}0$
2 $[2, 2, -w - 1]$ $\phantom{-}e$
5 $[5, 5, -w^{2} + w + 7]$ $-\frac{1}{2}e^{3} - e^{2} + 2e + 4$
5 $[5, 5, -w^{2} + w + 5]$ $\phantom{-}\frac{1}{2}e^{3} - 2e + 2$
17 $[17, 17, -w^{2} + 3w + 1]$ $\phantom{-}\frac{1}{2}e^{3} - 4e + 2$
23 $[23, 23, -w^{2} + w + 3]$ $-e^{3} + 8e$
27 $[27, 3, 3]$ $-2e^{2} - 2e + 8$
29 $[29, 29, -w^{2} + 3w - 1]$ $\phantom{-}\frac{1}{2}e^{3} + e^{2} - 4e$
37 $[37, 37, w^{2} + w + 1]$ $-\frac{3}{2}e^{3} - e^{2} + 10e$
41 $[41, 41, w^{2} - w - 9]$ $-\frac{3}{2}e^{3} - e^{2} + 8e + 4$
43 $[43, 43, -3w^{2} + 3w + 17]$ $\phantom{-}e^{3} + 2e^{2} - 8e - 8$
47 $[47, 47, 2w^{2} - 2w - 13]$ $-e^{3} - 2e^{2} + 6e + 4$
47 $[47, 47, -2w + 5]$ $\phantom{-}2e^{2} - 2e - 8$
53 $[53, 53, 3w^{2} - w - 19]$ $\phantom{-}\frac{3}{2}e^{3} - 8e - 2$
59 $[59, 59, 2w - 1]$ $\phantom{-}e^{3} - 10e$
67 $[67, 67, w^{2} + w - 5]$ $\phantom{-}2e^{2} + 2e - 12$
71 $[71, 71, -3w^{2} + w + 21]$ $\phantom{-}e^{3} - 4e - 4$
79 $[79, 79, 3w^{2} - w - 23]$ $\phantom{-}e^{3} - 6e + 8$
89 $[89, 89, 2w^{2} - 4w - 7]$ $-\frac{3}{2}e^{3} - 2e^{2} + 6e + 14$
89 $[89, 89, -2w^{2} - 2w + 5]$ $-\frac{1}{2}e^{3} + e^{2} + 6e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $-1$