Properties

Label 3.3.1509.1-12.2-g
Base field 3.3.1509.1
Weight $[2, 2, 2]$
Level norm $12$
Level $[12, 6, w^{2} - w - 9]$
Dimension $2$
CM no
Base change no

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Base field 3.3.1509.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 4\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[12, 6, w^{2} - w - 9]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $22$

Hecke eigenvalues ($q$-expansion)

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

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

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + 6]$ $\phantom{-}2$
3 $[3, 3, -2w^{2} + w + 15]$ $\phantom{-}e$
3 $[3, 3, w - 1]$ $-1$
4 $[4, 2, -w^{2} + 3w - 1]$ $-1$
11 $[11, 11, w + 3]$ $-2$
19 $[19, 19, -w^{2} + 5]$ $\phantom{-}3e + 2$
23 $[23, 23, -2w^{2} + 2w + 17]$ $-e - 5$
31 $[31, 31, -w^{2} + 2w + 1]$ $\phantom{-}1$
37 $[37, 37, 2w^{2} - 13]$ $-4e$
43 $[43, 43, 5w^{2} - 2w - 35]$ $-e$
43 $[43, 43, 3w - 1]$ $-4e$
43 $[43, 43, 2w - 3]$ $\phantom{-}e - 1$
47 $[47, 47, w^{2} - 3]$ $-e - 9$
59 $[59, 59, -3w^{2} + 2w + 21]$ $-3e - 5$
71 $[71, 71, 2w + 3]$ $\phantom{-}1$
71 $[71, 71, 3w^{2} - 19]$ $\phantom{-}e + 10$
71 $[71, 71, 4w^{2} - 13w + 5]$ $\phantom{-}3e + 4$
83 $[83, 83, 2w^{2} - 15]$ $-8e - 4$
89 $[89, 89, -w^{2} - 1]$ $-e - 16$
89 $[89, 89, 2w^{2} - 4w + 1]$ $-5e - 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w - 1]$ $1$
$4$ $[4, 2, -w^{2} + 3w - 1]$ $1$