Properties

Label 3.3.785.1-17.1-d
Base field 3.3.785.1
Weight $[2, 2, 2]$
Level norm $17$
Level $[17, 17, -w^{2} + w + 3]$
Dimension $6$
CM no
Base change no

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Base field 3.3.785.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 5\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[17, 17, -w^{2} + w + 3]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $15$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} - 5x^{5} - 2x^{4} + 31x^{3} - 2x^{2} - 54x - 13\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w - 2]$ $\phantom{-}e$
5 $[5, 5, w]$ $-e^{2} + 2e + 3$
5 $[5, 5, -w + 3]$ $\phantom{-}\frac{1}{2}e^{5} - 2e^{4} - e^{3} + \frac{15}{2}e^{2} + \frac{1}{2}e - \frac{5}{2}$
8 $[8, 2, 2]$ $-e + 2$
9 $[9, 3, w^{2} + w - 4]$ $-\frac{1}{2}e^{5} + e^{4} + 5e^{3} - \frac{9}{2}e^{2} - \frac{31}{2}e - \frac{5}{2}$
13 $[13, 13, w + 3]$ $-e^{4} + 4e^{3} + e^{2} - 12e + 2$
17 $[17, 17, -w^{2} + w + 3]$ $\phantom{-}1$
23 $[23, 23, w^{2} - 2]$ $-e^{3} + 2e^{2} + 3e$
23 $[23, 23, w^{2} - 3]$ $-e^{4} + 3e^{3} + 4e^{2} - 9e - 6$
23 $[23, 23, -w^{2} + 8]$ $\phantom{-}e^{5} - 2e^{4} - 10e^{3} + 8e^{2} + 31e + 10$
29 $[29, 29, w - 4]$ $-e^{5} + 4e^{4} + 2e^{3} - 13e^{2} - 3e + 1$
37 $[37, 37, w^{2} + w - 8]$ $\phantom{-}2e^{4} - 7e^{3} - 7e^{2} + 24e + 12$
41 $[41, 41, w^{2} + 2w - 4]$ $\phantom{-}e^{3} - e^{2} - 5e + 3$
47 $[47, 47, 2w^{2} + w - 8]$ $-\frac{1}{2}e^{5} + 3e^{4} - 2e^{3} - \frac{21}{2}e^{2} + \frac{17}{2}e + \frac{9}{2}$
59 $[59, 59, -2w^{2} - 3w + 6]$ $-e^{5} + 4e^{4} + 2e^{3} - 15e^{2} - e + 11$
61 $[61, 61, -2w - 1]$ $-e^{5} + 2e^{4} + 9e^{3} - 8e^{2} - 24e - 9$
67 $[67, 67, -2w - 3]$ $\phantom{-}e^{5} - 4e^{4} - 2e^{3} + 16e^{2} - e - 12$
79 $[79, 79, 2w^{2} - 9]$ $-\frac{1}{2}e^{5} - e^{4} + 13e^{3} - \frac{5}{2}e^{2} - \frac{73}{2}e - \frac{3}{2}$
109 $[109, 109, w^{2} + 2w - 6]$ $\phantom{-}e^{4} - 3e^{3} - 5e^{2} + 10e + 9$
109 $[109, 109, 2w^{2} + w - 14]$ $\phantom{-}2e^{5} - 9e^{4} + 2e^{3} + 27e^{2} - 19e - 8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$17$ $[17, 17, -w^{2} + w + 3]$ $-1$