Properties

Label 3.3.1509.1-8.1-a
Base field 3.3.1509.1
Weight $[2, 2, 2]$
Level norm $8$
Level $[8, 2, 2]$
Dimension $6$
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: $[8, 2, 2]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $12$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} - 3x^{5} - 11x^{4} + 36x^{3} + 11x^{2} - 56x - 14\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + 6]$ $-1$
3 $[3, 3, -2w^{2} + w + 15]$ $\phantom{-}e$
3 $[3, 3, w - 1]$ $-\frac{2}{3}e^{5} + \frac{1}{3}e^{4} + \frac{26}{3}e^{3} - \frac{10}{3}e^{2} - \frac{62}{3}e - \frac{16}{3}$
4 $[4, 2, -w^{2} + 3w - 1]$ $\phantom{-}1$
11 $[11, 11, w + 3]$ $\phantom{-}e^{5} - e^{4} - 12e^{3} + 10e^{2} + 22e + 4$
19 $[19, 19, -w^{2} + 5]$ $-e^{2} + 6$
23 $[23, 23, -2w^{2} + 2w + 17]$ $-e^{5} + e^{4} + 13e^{3} - 10e^{2} - 29e - 4$
31 $[31, 31, -w^{2} + 2w + 1]$ $\phantom{-}2e$
37 $[37, 37, 2w^{2} - 13]$ $\phantom{-}e^{5} - e^{4} - 11e^{3} + 12e^{2} + 13e - 6$
43 $[43, 43, 5w^{2} - 2w - 35]$ $-e^{5} + e^{4} + 12e^{3} - 12e^{2} - 22e + 6$
43 $[43, 43, 3w - 1]$ $\phantom{-}2e^{5} - e^{4} - 26e^{3} + 10e^{2} + 62e + 18$
43 $[43, 43, 2w - 3]$ $\phantom{-}e^{5} - e^{4} - 13e^{3} + 9e^{2} + 29e + 10$
47 $[47, 47, w^{2} - 3]$ $\phantom{-}2e^{5} - 2e^{4} - 24e^{3} + 22e^{2} + 42e + 2$
59 $[59, 59, -3w^{2} + 2w + 21]$ $-e^{5} + e^{4} + 13e^{3} - 10e^{2} - 28e - 2$
71 $[71, 71, 2w + 3]$ $-2e^{5} + 2e^{4} + 24e^{3} - 22e^{2} - 44e$
71 $[71, 71, 3w^{2} - 19]$ $\phantom{-}e^{5} - e^{4} - 13e^{3} + 10e^{2} + 33e$
71 $[71, 71, 4w^{2} - 13w + 5]$ $\phantom{-}e^{5} - e^{4} - 13e^{3} + 10e^{2} + 33e$
83 $[83, 83, 2w^{2} - 15]$ $\phantom{-}e^{5} - e^{4} - 13e^{3} + 10e^{2} + 30e$
89 $[89, 89, -w^{2} - 1]$ $\phantom{-}e^{4} - 2e^{3} - 12e^{2} + 18e + 22$
89 $[89, 89, 2w^{2} - 4w + 1]$ $\phantom{-}e^{2} - 2e - 8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w^{2} + 6]$ $1$
$4$ $[4, 2, -w^{2} + 3w - 1]$ $-1$