Properties

Label 3.3.1101.1-9.3-d
Base field 3.3.1101.1
Weight $[2, 2, 2]$
Level norm $9$
Level $[9, 9, 2w - 5]$
Dimension $2$
CM no
Base change no

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Base field 3.3.1101.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 12\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[9, 9, 2w - 5]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $12$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - x - 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w - 2]$ $\phantom{-}e$
3 $[3, 3, -w + 3]$ $\phantom{-}e$
3 $[3, 3, w - 1]$ $\phantom{-}0$
4 $[4, 2, w^{2} + w - 7]$ $\phantom{-}e$
19 $[19, 19, w + 1]$ $-2e - 3$
23 $[23, 23, w^{2} - 2w - 1]$ $-2e + 3$
31 $[31, 31, -2w^{2} + 19]$ $\phantom{-}4e - 3$
31 $[31, 31, -w^{2} + 5]$ $\phantom{-}e + 3$
31 $[31, 31, -3w + 5]$ $-e - 8$
41 $[41, 41, w^{2} + 2w - 7]$ $-2e + 3$
43 $[43, 43, w^{2} - 11]$ $-5e + 3$
47 $[47, 47, 3w - 7]$ $\phantom{-}9$
53 $[53, 53, -3w^{2} - 6w + 11]$ $\phantom{-}e + 3$
59 $[59, 59, 2w - 1]$ $\phantom{-}5e - 3$
67 $[67, 67, 2w^{2} + w - 19]$ $\phantom{-}3e + 4$
67 $[67, 67, 3w^{2} + 2w - 25]$ $\phantom{-}2e - 6$
67 $[67, 67, w - 5]$ $\phantom{-}0$
73 $[73, 73, -4w^{2} - 3w + 29]$ $-2e - 9$
73 $[73, 73, 2w^{2} - w - 11]$ $\phantom{-}3$
73 $[73, 73, w^{2} + 2w - 11]$ $-2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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