Properties

Label 3.3.469.1-17.1-b
Base field 3.3.469.1
Weight $[2, 2, 2]$
Level norm $17$
Level $[17, 17, w + 3]$
Dimension $7$
CM no
Base change no

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Base field 3.3.469.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 5x + 4\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[17, 17, w + 3]$
Dimension: $7$
CM: no
Base change: no
Newspace dimension: $9$

Hecke eigenvalues ($q$-expansion)

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

\(x^{7} - 2x^{6} - 9x^{5} + 13x^{4} + 25x^{3} - 17x^{2} - 16x + 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 2]$ $\phantom{-}e$
4 $[4, 2, -w^{2} - w + 3]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{1}{2}e^{4} - \frac{7}{2}e^{3} + \frac{3}{2}e^{2} + \frac{11}{2}e + \frac{1}{2}$
7 $[7, 7, w + 1]$ $-\frac{1}{2}e^{6} + e^{5} + 4e^{4} - 6e^{3} - 8e^{2} + 5e + \frac{1}{2}$
7 $[7, 7, -w + 3]$ $-e^{4} + e^{3} + 5e^{2} - 2e - 1$
11 $[11, 11, -w^{2} + 3]$ $-\frac{1}{2}e^{5} + \frac{1}{2}e^{4} + \frac{5}{2}e^{3} - \frac{3}{2}e^{2} + \frac{1}{2}e + \frac{3}{2}$
17 $[17, 17, w + 3]$ $\phantom{-}1$
19 $[19, 19, w^{2} - 7]$ $-e^{6} + \frac{5}{2}e^{5} + \frac{13}{2}e^{4} - \frac{29}{2}e^{3} - \frac{23}{2}e^{2} + \frac{31}{2}e + \frac{7}{2}$
27 $[27, 3, 3]$ $\phantom{-}\frac{1}{2}e^{6} - e^{5} - 3e^{4} + 5e^{3} + 3e^{2} - 5e + \frac{5}{2}$
43 $[43, 43, -2w - 5]$ $-\frac{1}{2}e^{6} + \frac{1}{2}e^{5} + \frac{11}{2}e^{4} - \frac{7}{2}e^{3} - \frac{33}{2}e^{2} + \frac{11}{2}e + 8$
47 $[47, 47, 2w + 3]$ $-\frac{1}{2}e^{5} + \frac{5}{2}e^{4} + \frac{5}{2}e^{3} - \frac{27}{2}e^{2} - \frac{15}{2}e + \frac{15}{2}$
53 $[53, 53, 3w^{2} + 2w - 9]$ $-e^{5} + e^{4} + 9e^{3} - 5e^{2} - 19e + 3$
59 $[59, 59, 2w^{2} + w - 5]$ $\phantom{-}\frac{3}{2}e^{5} - \frac{7}{2}e^{4} - \frac{15}{2}e^{3} + \frac{29}{2}e^{2} + \frac{13}{2}e - \frac{9}{2}$
61 $[61, 61, 3w - 1]$ $-e^{6} + 2e^{5} + 8e^{4} - 12e^{3} - 18e^{2} + 14e + 5$
61 $[61, 61, 2w^{2} + w - 9]$ $-\frac{1}{2}e^{6} + 7e^{4} - e^{3} - 25e^{2} + \frac{31}{2}$
61 $[61, 61, 2w^{2} - w - 7]$ $\phantom{-}e^{6} - 2e^{5} - 7e^{4} + 14e^{3} + 9e^{2} - 24e - 1$
67 $[67, 67, -2w^{2} + 13]$ $\phantom{-}\frac{1}{2}e^{6} - e^{5} - 2e^{4} + 4e^{3} - 2e^{2} - 3e + \frac{7}{2}$
67 $[67, 67, -3w - 7]$ $-\frac{1}{2}e^{6} + 2e^{5} + e^{4} - 13e^{3} + 7e^{2} + 22e - \frac{17}{2}$
73 $[73, 73, w^{2} + 2w - 5]$ $\phantom{-}\frac{1}{2}e^{6} - \frac{3}{2}e^{5} - \frac{7}{2}e^{4} + \frac{21}{2}e^{3} + \frac{17}{2}e^{2} - \frac{37}{2}e - 7$
79 $[79, 79, w - 5]$ $\phantom{-}\frac{1}{2}e^{6} - \frac{3}{2}e^{5} - \frac{7}{2}e^{4} + \frac{21}{2}e^{3} + \frac{13}{2}e^{2} - \frac{29}{2}e + 5$
83 $[83, 83, -2w^{2} + 4w + 3]$ $-\frac{1}{2}e^{6} + \frac{1}{2}e^{5} + \frac{11}{2}e^{4} - \frac{3}{2}e^{3} - \frac{41}{2}e^{2} - \frac{13}{2}e + 18$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$17$ $[17, 17, w + 3]$ $-1$