Properties

Label 3.3.1509.1-9.1-a
Base field 3.3.1509.1
Weight $[2, 2, 2]$
Level norm $9$
Level $[9, 3, w^{2} - 2w + 1]$
Dimension $4$
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: $[9, 3, w^{2} - 2w + 1]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $18$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - x^{3} - 5x^{2} + 2x + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + 6]$ $\phantom{-}e$
3 $[3, 3, -2w^{2} + w + 15]$ $-e^{3} + e^{2} + 5e - 1$
3 $[3, 3, w - 1]$ $\phantom{-}0$
4 $[4, 2, -w^{2} + 3w - 1]$ $\phantom{-}e^{2} - e - 3$
11 $[11, 11, w + 3]$ $\phantom{-}e^{3} - e^{2} - 6e + 4$
19 $[19, 19, -w^{2} + 5]$ $-e^{3} + 2e^{2} + 6e - 5$
23 $[23, 23, -2w^{2} + 2w + 17]$ $-e^{3} + e^{2} + 6e$
31 $[31, 31, -w^{2} + 2w + 1]$ $\phantom{-}e^{3} - 2e^{2} - 6e + 1$
37 $[37, 37, 2w^{2} - 13]$ $\phantom{-}4e^{3} - 3e^{2} - 18e + 3$
43 $[43, 43, 5w^{2} - 2w - 35]$ $-5e^{3} + 5e^{2} + 22e - 4$
43 $[43, 43, 3w - 1]$ $-2e^{3} + 4e^{2} + 7e - 7$
43 $[43, 43, 2w - 3]$ $-2e^{3} + e^{2} + 14e - 1$
47 $[47, 47, w^{2} - 3]$ $-e + 3$
59 $[59, 59, -3w^{2} + 2w + 21]$ $\phantom{-}5e^{3} - 4e^{2} - 20e + 5$
71 $[71, 71, 2w + 3]$ $-e^{3} - e^{2} + 2e + 14$
71 $[71, 71, 3w^{2} - 19]$ $\phantom{-}3e^{3} - 5e^{2} - 16e + 12$
71 $[71, 71, 4w^{2} - 13w + 5]$ $-e^{3} + e^{2} + 3e - 7$
83 $[83, 83, 2w^{2} - 15]$ $-5e^{3} + 3e^{2} + 23e - 5$
89 $[89, 89, -w^{2} - 1]$ $-4e^{3} + 3e^{2} + 16e - 1$
89 $[89, 89, 2w^{2} - 4w + 1]$ $\phantom{-}2e^{3} - 10e - 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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