Properties

Label 3.3.1772.1-9.2-b
Base field 3.3.1772.1
Weight $[2, 2, 2]$
Level norm $9$
Level $[9, 9, w^{2} - 5w + 3]$
Dimension $3$
CM no
Base change no

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Base field 3.3.1772.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 12x + 8\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[9, 9, w^{2} - 5w + 3]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $24$

Hecke eigenvalues ($q$-expansion)

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

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

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -\frac{1}{2}w^{2} - \frac{1}{2}w + 4]$ $\phantom{-}e$
2 $[2, 2, -w^{2} + 11]$ $\phantom{-}e^{2} - 2e$
3 $[3, 3, -\frac{1}{2}w^{2} + \frac{1}{2}w + 7]$ $\phantom{-}0$
5 $[5, 5, -\frac{3}{2}w^{2} - \frac{1}{2}w + 15]$ $-2e^{2} + 5e$
9 $[9, 3, -\frac{1}{2}w^{2} + \frac{5}{2}w - 1]$ $-2e^{2} + 5e + 2$
25 $[25, 5, \frac{7}{2}w^{2} - \frac{31}{2}w + 9]$ $-6e^{2} + 15e - 1$
29 $[29, 29, -\frac{5}{2}w^{2} + \frac{1}{2}w + 29]$ $\phantom{-}4e^{2} - 10e - 2$
41 $[41, 41, -w^{2} + 3w - 1]$ $\phantom{-}3e^{2} - 3e - 7$
41 $[41, 41, -\frac{1}{2}w^{2} - \frac{3}{2}w + 3]$ $-e^{2} + e - 3$
41 $[41, 41, 2w + 7]$ $\phantom{-}3e - 3$
43 $[43, 43, -\frac{7}{2}w^{2} - \frac{1}{2}w + 37]$ $-3e^{2} + 10e + 1$
43 $[43, 43, \frac{1}{2}w^{2} - \frac{9}{2}w + 3]$ $\phantom{-}3e - 10$
43 $[43, 43, \frac{1}{2}w^{2} - \frac{1}{2}w + 1]$ $-6e^{2} + 18e - 4$
47 $[47, 47, -w^{2} + w + 15]$ $-4e^{2} + 14e - 4$
53 $[53, 53, -2w^{2} + 2w + 29]$ $\phantom{-}e^{2} - 2e + 3$
59 $[59, 59, w^{2} - w - 13]$ $\phantom{-}e^{2} - 5e + 8$
67 $[67, 67, -\frac{1}{2}w^{2} + \frac{1}{2}w + 9]$ $\phantom{-}2e^{2} - 8e + 3$
71 $[71, 71, 2w - 3]$ $-e^{2} - 5e + 7$
73 $[73, 73, \frac{3}{2}w^{2} - \frac{11}{2}w + 1]$ $-e^{2} - 3e + 13$
79 $[79, 79, -\frac{3}{2}w^{2} + \frac{15}{2}w - 5]$ $-6e^{2} + 19e - 1$
Display number of eigenvalues

Atkin-Lehner eigenvalues

The Atkin-Lehner eigenvalues for this form are not in the database.