Properties

Label 4.4.19429.1-7.1-b
Base field 4.4.19429.1
Weight $[2, 2, 2, 2]$
Level norm $7$
Level $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$
Dimension $3$
CM no
Base change no

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Base field 4.4.19429.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $15$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} + x^{2} - 7x - 8\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}0$
5 $[5, 5, w]$ $\phantom{-}e$
7 $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ $\phantom{-}1$
13 $[13, 13, -w^{2} + w + 4]$ $-e^{2} + 4$
13 $[13, 13, -w^{3} + 2w^{2} + 5w - 2]$ $-e^{2} + 2e + 6$
16 $[16, 2, 2]$ $-1$
17 $[17, 17, -w + 2]$ $-e^{2} + 2$
19 $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}2e^{2} - 2e - 12$
27 $[27, 3, w^{3} - 3w^{2} - 4w + 7]$ $-2e^{2} + 8$
31 $[31, 31, w^{3} - 3w^{2} - 3w + 7]$ $\phantom{-}2e^{2} - 2e - 10$
31 $[31, 31, -w^{3} + w^{2} + 6w + 1]$ $\phantom{-}2e^{2} - 2e - 12$
41 $[41, 41, w^{2} - w - 1]$ $-3e - 2$
43 $[43, 43, 2w^{3} - 5w^{2} - 6w + 4]$ $\phantom{-}2$
47 $[47, 47, -w^{3} + 2w^{2} + 5w - 1]$ $-2e^{2} + 2e + 12$
53 $[53, 53, -w - 3]$ $-3e - 2$
53 $[53, 53, -w^{3} + 3w^{2} + 3w - 6]$ $-e + 2$
59 $[59, 59, 2w^{2} - 3w - 6]$ $-4$
59 $[59, 59, w^{3} - w^{2} - 7w - 3]$ $\phantom{-}2e^{2} + 2e - 10$
79 $[79, 79, 2w^{3} - 4w^{2} - 8w + 3]$ $\phantom{-}2e^{2} - 10$
79 $[79, 79, w^{2} - 2w - 1]$ $-2e^{2} - 2e + 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$7$ $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ $-1$