Properties

Label 4.4.19796.1-10.1-b
Base field 4.4.19796.1
Weight $[2, 2, 2, 2]$
Level norm $10$
Level $[10, 10, -w^{3} + 2w^{2} + 4w - 3]$
Dimension $4$
CM no
Base change no

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Base field 4.4.19796.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + x + 8\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[10, 10, -w^{3} + 2w^{2} + 4w - 3]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $18$

Hecke eigenvalues ($q$-expansion)

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

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

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + 2]$ $\phantom{-}e$
2 $[2, 2, -w^{3} + 2w^{2} + 4w - 5]$ $-1$
5 $[5, 5, -w^{3} + 2w^{2} + 3w - 1]$ $-1$
13 $[13, 13, w^{3} - 2w^{2} - 3w + 5]$ $\phantom{-}e^{2} + 2e - 4$
17 $[17, 17, -w^{2} - w + 3]$ $-e^{3} - e^{2} + 6e + 3$
19 $[19, 19, -w^{3} + 3w^{2} + 2w - 7]$ $-e^{2} - 2e + 5$
23 $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ $-3e^{3} - 4e^{2} + 11e + 6$
31 $[31, 31, -w^{2} + w + 1]$ $-3e^{3} - 5e^{2} + 12e + 8$
47 $[47, 47, -w^{3} + w^{2} + 4w - 3]$ $\phantom{-}e^{3} - 8e + 3$
49 $[49, 7, 2w^{3} - 5w^{2} - 7w + 11]$ $-e^{3} - e^{2} + 3e + 8$
53 $[53, 53, -3w^{3} + 9w^{2} + 10w - 31]$ $\phantom{-}5e^{3} + 7e^{2} - 19e - 9$
53 $[53, 53, w^{3} - w^{2} - 4w + 1]$ $-3e^{3} - 4e^{2} + 13e + 3$
61 $[61, 61, 3w^{3} - 6w^{2} - 13w + 13]$ $-e^{3} + 2e^{2} + 8e - 4$
61 $[61, 61, 2w^{2} - 7]$ $-2e^{3} - 2e^{2} + 9e + 5$
71 $[71, 71, w^{2} - 3w - 5]$ $-2e^{3} + e^{2} + 11e - 6$
73 $[73, 73, 2w - 3]$ $-4e^{3} + 21e - 4$
73 $[73, 73, -2w^{3} + 6w^{2} + 6w - 19]$ $\phantom{-}2e^{3} + 3e^{2} - 7e - 4$
79 $[79, 79, 2w^{2} - 5]$ $-4e^{3} - 4e^{2} + 18e + 5$
81 $[81, 3, -3]$ $-2e^{3} - e^{2} + 10e - 5$
101 $[101, 101, 2w^{2} - 4w - 9]$ $\phantom{-}5e^{3} + 6e^{2} - 24e - 6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w^{3} + 2w^{2} + 4w - 5]$ $1$
$5$ $[5, 5, -w^{3} + 2w^{2} + 3w - 1]$ $1$