Properties

Base field 3.3.761.1
Weight [2, 2, 2]
Level norm 13
Level $[13, 13, -w^{2} + w + 4]$
Label 3.3.761.1-13.1-a
Dimension 5
CM no
Base change no

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Base field 3.3.761.1

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

Form

Weight [2, 2, 2]
Level $[13, 13, -w^{2} + w + 4]$
Label 3.3.761.1-13.1-a
Dimension 5
Is CM no
Is base change no
Parent newspace dimension 10

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} - 5x^{4} + 3x^{3} + 13x^{2} - 9x - 8\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}e$
7 $[7, 7, w - 1]$ $-e^{3} + e^{2} + 4e$
8 $[8, 2, 2]$ $-e^{4} + 3e^{3} + 2e^{2} - 7e - 1$
9 $[9, 3, -w^{2} + 2w + 4]$ $\phantom{-}e^{4} - 2e^{3} - 5e^{2} + 6e + 8$
11 $[11, 11, -w^{2} + 2w + 2]$ $-e^{3} + 3e^{2} - 2$
13 $[13, 13, -w^{2} + w + 4]$ $\phantom{-}1$
19 $[19, 19, w + 3]$ $\phantom{-}e^{4} - 3e^{3} + e^{2} + e - 4$
19 $[19, 19, -w^{2} + 2w + 5]$ $-e^{4} + 2e^{3} + 5e^{2} - 7e - 4$
19 $[19, 19, -w^{2} + 3w + 2]$ $-2e^{3} + 4e^{2} + 4e - 2$
23 $[23, 23, w^{2} - w - 3]$ $-2e^{4} + 7e^{3} + 3e^{2} - 17e - 2$
23 $[23, 23, -w^{2} + 2]$ $\phantom{-}e^{4} - 2e^{3} - 3e^{2} + 2e + 6$
23 $[23, 23, -w + 4]$ $\phantom{-}2e^{4} - 5e^{3} - 8e^{2} + 12e + 12$
31 $[31, 31, w^{2} - 5]$ $-e^{4} + 5e^{3} - 2e^{2} - 10e$
43 $[43, 43, w^{2} - 3w - 3]$ $\phantom{-}e^{3} - 3e^{2} - e + 2$
49 $[49, 7, w^{2} - 6]$ $-2e^{4} + 5e^{3} + 10e^{2} - 15e - 18$
53 $[53, 53, 2w - 5]$ $-e^{4} + 3e^{3} - e + 2$
61 $[61, 61, 2w^{2} - 2w - 9]$ $\phantom{-}2e^{4} - 3e^{3} - 14e^{2} + 9e + 20$
71 $[71, 71, 2w - 3]$ $\phantom{-}2e^{4} - 9e^{3} + 7e^{2} + 13e - 8$
73 $[73, 73, 2w^{2} - 5w - 5]$ $-3e^{4} + 9e^{3} + 3e^{2} - 13e$
83 $[83, 83, w^{2} - w - 9]$ $-4e^{4} + 9e^{3} + 13e^{2} - 16e - 12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
13 $[13, 13, -w^{2} + w + 4]$ $-1$