Properties

Label 3.3.1076.1-9.1-c
Base field 3.3.1076.1
Weight $[2, 2, 2]$
Level norm $9$
Level $[9, 3, -w^{2} + 5]$
Dimension $4$
CM no
Base change no

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Base field 3.3.1076.1

Generator \(w\), with minimal polynomial \(x^{3} - 8x - 6\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[9, 3, -w^{2} + 5]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $14$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} + x^{3} - 5x^{2} - 4x + 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $\phantom{-}e$
3 $[3, 3, -w^{2} + 2w + 3]$ $-e + 1$
7 $[7, 7, -2w^{2} + 5w + 5]$ $-e^{3} + 4e + 3$
9 $[9, 3, -w^{2} + 5]$ $\phantom{-}1$
13 $[13, 13, -w^{2} + 3w + 1]$ $\phantom{-}2e^{3} + e^{2} - 7e - 2$
13 $[13, 13, 2w + 5]$ $\phantom{-}e^{2} - 1$
13 $[13, 13, w - 1]$ $\phantom{-}e^{2} + e - 4$
17 $[17, 17, w^{2} - w - 5]$ $\phantom{-}e^{3} - e^{2} - 4e + 4$
19 $[19, 19, w^{2} - 2w - 5]$ $\phantom{-}e^{3} - 3e^{2} - 5e + 9$
29 $[29, 29, w^{2} - 7]$ $\phantom{-}e^{3} - 2e^{2} - 3e + 10$
31 $[31, 31, 2w^{2} - 3w - 11]$ $\phantom{-}3e^{3} - 10e + 1$
49 $[49, 7, -2w^{2} - 4w + 1]$ $-2e^{3} - e^{2} + 6e + 5$
59 $[59, 59, w^{2} - 2w - 11]$ $\phantom{-}3e^{3} - 14e - 5$
71 $[71, 71, -2w + 7]$ $-4e^{3} + 2e^{2} + 13e - 9$
73 $[73, 73, w^{2} - 3w - 13]$ $-4e^{3} - 3e^{2} + 19e + 6$
73 $[73, 73, 2w^{2} - 2w - 17]$ $-2e + 4$
73 $[73, 73, -w^{2} - 4w - 5]$ $-4e^{3} + e^{2} + 15e - 8$
79 $[79, 79, 2w - 1]$ $\phantom{-}e - 3$
79 $[79, 79, w^{2} + w - 5]$ $-3e^{3} + 3e^{2} + 16e - 8$
79 $[79, 79, w - 5]$ $-2e^{3} + e^{2} + 10e + 7$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$9$ $[9, 3, -w^{2} + 5]$ $-1$