Properties

Label 3.3.1257.1-9.1-c
Base field 3.3.1257.1
Weight $[2, 2, 2]$
Level norm $9$
Level $[9, 3, w^{2} + w - 6]$
Dimension $2$
CM no
Base change no

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Base field 3.3.1257.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x + 9\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[9, 3, w^{2} + w - 6]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $6$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} + 2x - 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w + 3]$ $-1$
3 $[3, 3, w - 2]$ $-1$
5 $[5, 5, w^{2} + w - 5]$ $\phantom{-}e$
8 $[8, 2, 2]$ $\phantom{-}1$
13 $[13, 13, w + 2]$ $-2e - 2$
13 $[13, 13, -2w + 5]$ $-e$
13 $[13, 13, -w^{2} - w + 4]$ $-e - 4$
19 $[19, 19, -w^{2} + w + 4]$ $\phantom{-}0$
23 $[23, 23, -w^{2} - w + 7]$ $-4$
25 $[25, 5, w^{2} - 2w - 1]$ $\phantom{-}e + 8$
29 $[29, 29, w^{2} - 5]$ $\phantom{-}e - 4$
31 $[31, 31, w^{2} + w - 8]$ $\phantom{-}2e$
41 $[41, 41, w^{2} + w - 11]$ $-2e + 2$
47 $[47, 47, w^{2} + 2w - 1]$ $\phantom{-}4e + 8$
59 $[59, 59, w^{2} + w - 1]$ $\phantom{-}4e + 4$
61 $[61, 61, -w^{2} + 5w - 7]$ $\phantom{-}2e - 2$
67 $[67, 67, 2w^{2} - 13]$ $-8$
89 $[89, 89, -2w^{2} + w + 20]$ $\phantom{-}6e + 2$
89 $[89, 89, 5w^{2} + 8w - 19]$ $-5e$
89 $[89, 89, w^{2} + 2w - 7]$ $\phantom{-}3e - 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, -w + 3]$ $1$
$3$ $[3, 3, w - 2]$ $1$