Properties

Label 3.3.404.1-9.1-a
Base field 3.3.404.1
Weight $[2, 2, 2]$
Level norm $9$
Level $[9, 3, w^{2} - 2]$
Dimension $3$
CM no
Base change no

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Base field 3.3.404.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 5x - 1\); narrow class number \(1\) and class number \(1\).

Form

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

Hecke eigenvalues ($q$-expansion)

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

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

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 1]$ $\phantom{-}e$
3 $[3, 3, w^{2} - 2w - 2]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}$
7 $[7, 7, -w + 2]$ $-\frac{1}{2}e^{2} + \frac{5}{2}$
9 $[9, 3, w^{2} - 2]$ $\phantom{-}1$
11 $[11, 11, -w^{2} + 2w + 4]$ $\phantom{-}e - 1$
29 $[29, 29, -2w + 1]$ $\phantom{-}\frac{3}{2}e^{2} + 4e - \frac{11}{2}$
37 $[37, 37, 2w^{2} - 4w - 3]$ $-3e^{2} - 5e + 10$
37 $[37, 37, -w^{2} + 3w + 3]$ $-\frac{3}{2}e^{2} - 2e + \frac{15}{2}$
37 $[37, 37, 2w^{2} - w - 8]$ $-\frac{3}{2}e^{2} - 4e + \frac{7}{2}$
41 $[41, 41, w^{2} - 4w + 2]$ $-\frac{1}{2}e^{2} + \frac{13}{2}$
43 $[43, 43, -2w^{2} + 2w + 7]$ $\phantom{-}e^{2} - 5$
43 $[43, 43, -2w^{2} + 3w + 6]$ $-\frac{1}{2}e^{2} - 4e + \frac{1}{2}$
43 $[43, 43, -w^{2} + 6]$ $-e^{2} - 4e + 5$
49 $[49, 7, w^{2} + w - 3]$ $\phantom{-}3e^{2} + 2e - 3$
53 $[53, 53, 2w^{2} - 5w - 4]$ $-2e^{2} + 12$
59 $[59, 59, 2w - 3]$ $\phantom{-}e + 7$
61 $[61, 61, -w - 4]$ $-2e^{2} - 2e + 6$
67 $[67, 67, -2w^{2} - w + 2]$ $-4e^{2} - 2e + 10$
73 $[73, 73, 2w^{2} - 3w - 12]$ $\phantom{-}4e + 2$
83 $[83, 83, -2w - 5]$ $\phantom{-}4e^{2} + 6e - 10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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