Properties

Base field 3.3.761.1
Weight [2, 2, 2]
Level norm 7
Level $[7, 7, w - 1]$
Label 3.3.761.1-7.1-a
Dimension 4
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 $[7, 7, w - 1]$
Label 3.3.761.1-7.1-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:
\(x^{4} - 10x^{2} + 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}e$
7 $[7, 7, w - 1]$ $\phantom{-}1$
8 $[8, 2, 2]$ $-e^{2} + 5$
9 $[9, 3, -w^{2} + 2w + 4]$ $\phantom{-}0$
11 $[11, 11, -w^{2} + 2w + 2]$ $-e^{3} + 9e$
13 $[13, 13, -w^{2} + w + 4]$ $\phantom{-}e$
19 $[19, 19, w + 3]$ $\phantom{-}0$
19 $[19, 19, -w^{2} + 2w + 5]$ $\phantom{-}0$
19 $[19, 19, -w^{2} + 3w + 2]$ $\phantom{-}e^{3} - 11e$
23 $[23, 23, w^{2} - w - 3]$ $\phantom{-}e^{3} - 10e$
23 $[23, 23, -w^{2} + 2]$ $\phantom{-}e$
23 $[23, 23, -w + 4]$ $\phantom{-}4$
31 $[31, 31, w^{2} - 5]$ $\phantom{-}e^{2} - 4$
43 $[43, 43, w^{2} - 3w - 3]$ $-e^{3} + 12e$
49 $[49, 7, w^{2} - 6]$ $-e^{2} + 6$
53 $[53, 53, 2w - 5]$ $\phantom{-}e^{2} - 2$
61 $[61, 61, 2w^{2} - 2w - 9]$ $-2e$
71 $[71, 71, 2w - 3]$ $-8$
73 $[73, 73, 2w^{2} - 5w - 5]$ $\phantom{-}2e^{3} - 16e$
83 $[83, 83, w^{2} - w - 9]$ $-2e^{2} + 16$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, w - 1]$ $-1$