Properties

Label 3.3.1620.1-7.1-c
Base field 3.3.1620.1
Weight $[2, 2, 2]$
Level norm $7$
Level $[7, 7, -w^{2} + 2w + 7]$
Dimension $2$
CM no
Base change no

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Base field 3.3.1620.1

Generator \(w\), with minimal polynomial \(x^{3} - 12x - 14\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[7, 7, -w^{2} + 2w + 7]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $25$

Hecke eigenvalues ($q$-expansion)

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

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

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $\phantom{-}e$
3 $[3, 3, w + 1]$ $\phantom{-}e - 2$
5 $[5, 5, -w - 3]$ $-e + 2$
5 $[5, 5, -2w^{2} + 3w + 19]$ $-2e + 2$
7 $[7, 7, -w^{2} + 2w + 7]$ $\phantom{-}1$
13 $[13, 13, w^{2} - 3w - 5]$ $\phantom{-}2e$
17 $[17, 17, w^{2} - w - 3]$ $\phantom{-}4$
23 $[23, 23, -w + 3]$ $\phantom{-}e + 2$
37 $[37, 37, 3w + 5]$ $-3e + 2$
43 $[43, 43, w^{2} + 3w + 3]$ $\phantom{-}2e$
47 $[47, 47, -w^{2} + 3]$ $\phantom{-}4e$
49 $[49, 7, -w^{2} + 5]$ $-e + 2$
53 $[53, 53, -w^{2} + w + 13]$ $\phantom{-}e + 2$
61 $[61, 61, -w^{2} + 15]$ $-2e$
61 $[61, 61, w^{2} - 2w - 13]$ $\phantom{-}2e - 10$
61 $[61, 61, -4w - 5]$ $-8$
67 $[67, 67, -2w^{2} + 6w + 13]$ $-7e + 6$
73 $[73, 73, 2w^{2} - 2w - 17]$ $\phantom{-}3e - 2$
79 $[79, 79, -w - 5]$ $\phantom{-}4e + 4$
79 $[79, 79, 2w^{2} - 4w - 17]$ $-5e + 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$7$ $[7, 7, -w^{2} + 2w + 7]$ $-1$