Properties

Label 3.3.1929.1-9.3-a
Base field 3.3.1929.1
Weight $[2, 2, 2]$
Level norm $9$
Level $[9, 9, 2w^{2} + w - 19]$
Dimension $2$
CM no
Base change no

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Base field 3.3.1929.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x + 13\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[9, 9, 2w^{2} + w - 19]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $20$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 6\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w - 2]$ $\phantom{-}0$
3 $[3, 3, w - 1]$ $\phantom{-}e$
7 $[7, 7, w^{2} + w - 7]$ $\phantom{-}e$
7 $[7, 7, -w^{2} + 11]$ $\phantom{-}4$
7 $[7, 7, -w^{2} + 9]$ $-2e$
8 $[8, 2, 2]$ $\phantom{-}3$
13 $[13, 13, -w]$ $\phantom{-}e$
19 $[19, 19, -w^{2} - w + 4]$ $\phantom{-}3e$
23 $[23, 23, w^{2} + w - 10]$ $-6$
29 $[29, 29, 2w^{2} - 21]$ $\phantom{-}e$
37 $[37, 37, 2w^{2} + w - 17]$ $\phantom{-}2e$
43 $[43, 43, 3w^{2} + 3w - 22]$ $\phantom{-}2e$
47 $[47, 47, w^{2} - 6]$ $-e$
47 $[47, 47, w^{2} - 3]$ $-e$
47 $[47, 47, -w^{2} + 12]$ $-12$
53 $[53, 53, w^{2} - w - 4]$ $-3e$
61 $[61, 61, w^{2} - 5]$ $-6e$
67 $[67, 67, w^{2} - w - 7]$ $-5e$
73 $[73, 73, 7w^{2} + 3w - 66]$ $\phantom{-}2$
79 $[79, 79, 2w^{2} - 19]$ $-2e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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