Properties

Label 4.4.5125.1-45.1-a
Base field 4.4.5125.1
Weight $[2, 2, 2, 2]$
Level norm $45$
Level $[45, 15, -w^{3} + 3w^{2} + 2w - 6]$
Dimension $2$
CM no
Base change no

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Base field 4.4.5125.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 6x^{2} + 7x + 11\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[45, 15, -w^{3} + 3w^{2} + 2w - 6]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $10$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 2x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -w^{2} + 2w + 3]$ $-1$
9 $[9, 3, w^{3} - 3w^{2} - 2w + 9]$ $\phantom{-}1$
9 $[9, 3, -w^{3} + 5w + 5]$ $\phantom{-}e$
11 $[11, 11, w]$ $-2e + 1$
11 $[11, 11, w - 1]$ $\phantom{-}e - 3$
16 $[16, 2, 2]$ $-e$
19 $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}e - 7$
19 $[19, 19, w^{3} - w^{2} - 4w + 2]$ $\phantom{-}3e - 4$
29 $[29, 29, w^{3} - 4w^{2} - w + 10]$ $-3e - 3$
29 $[29, 29, -w^{3} + 3w^{2} + w - 7]$ $-2e + 4$
41 $[41, 41, 3w^{2} - 2w - 10]$ $-2e + 3$
49 $[49, 7, -2w^{2} + 3w + 8]$ $\phantom{-}4e - 1$
49 $[49, 7, w^{3} - 2w^{2} - 2w + 5]$ $\phantom{-}2e - 7$
71 $[71, 71, -w - 3]$ $-8e + 5$
71 $[71, 71, w - 4]$ $\phantom{-}3e - 4$
79 $[79, 79, -w^{3} + w^{2} + 3w + 3]$ $-3e + 1$
79 $[79, 79, -w^{3} + 2w^{2} + 2w - 6]$ $-7e + 1$
89 $[89, 89, w^{3} - 3w^{2} - 3w + 7]$ $\phantom{-}6e - 15$
89 $[89, 89, w^{3} - 6w - 2]$ $-4e + 1$
101 $[101, 101, 2w^{3} - 5w^{2} - 3w + 9]$ $-6e + 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, -w^{2} + 2w + 3]$ $1$
$9$ $[9, 3, w^{3} - 3w^{2} - 2w + 9]$ $-1$