Properties

Base field 3.3.761.1
Weight [2, 2, 2]
Level norm 21
Level $[21, 21, w^{2} - 2w - 6]$
Label 3.3.761.1-21.1-e
Dimension 3
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 $[21, 21, w^{2} - 2w - 6]$
Label 3.3.761.1-21.1-e
Dimension 3
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:
\(x^{3} - 2x^{2} - 32x + 80\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $-1$
7 $[7, 7, w - 1]$ $\phantom{-}1$
8 $[8, 2, 2]$ $-1$
9 $[9, 3, -w^{2} + 2w + 4]$ $\phantom{-}e$
11 $[11, 11, -w^{2} + 2w + 2]$ $-\frac{1}{4}e^{2} - e + 8$
13 $[13, 13, -w^{2} + w + 4]$ $\phantom{-}\frac{1}{4}e^{2} - 4$
19 $[19, 19, w + 3]$ $\phantom{-}\frac{1}{4}e^{2} + e - 10$
19 $[19, 19, -w^{2} + 2w + 5]$ $-\frac{1}{4}e^{2} - e + 10$
19 $[19, 19, -w^{2} + 3w + 2]$ $\phantom{-}\frac{1}{2}e^{2} - 10$
23 $[23, 23, w^{2} - w - 3]$ $\phantom{-}\frac{1}{4}e^{2} + e - 4$
23 $[23, 23, -w^{2} + 2]$ $\phantom{-}6$
23 $[23, 23, -w + 4]$ $\phantom{-}\frac{1}{4}e^{2} - e - 6$
31 $[31, 31, w^{2} - 5]$ $-\frac{1}{2}e^{2} + 12$
43 $[43, 43, w^{2} - 3w - 3]$ $\phantom{-}6$
49 $[49, 7, w^{2} - 6]$ $\phantom{-}\frac{3}{4}e^{2} + e - 20$
53 $[53, 53, 2w - 5]$ $-\frac{1}{2}e^{2} + 14$
61 $[61, 61, 2w^{2} - 2w - 9]$ $-\frac{3}{4}e^{2} + 18$
71 $[71, 71, 2w - 3]$ $-\frac{1}{2}e^{2} + 12$
73 $[73, 73, 2w^{2} - 5w - 5]$ $-\frac{1}{2}e^{2} - e + 16$
83 $[83, 83, w^{2} - w - 9]$ $-e^{2} - 2e + 24$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $1$
7 $[7, 7, w - 1]$ $-1$