Properties

Label 6.6.1995125.1-29.2-c
Base field 6.6.1995125.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $29$
Level $[29, 29, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 6w - 2]$
Dimension $4$
CM no
Base change no

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Base field 6.6.1995125.1

Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 6x^{4} + 6x^{3} + 12x^{2} + x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[29, 29, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 6w - 2]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $40$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} + 2x^{3} - 10x^{2} - 11x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
11 $[11, 11, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w + 2]$ $-e + 2$
11 $[11, 11, w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 4w - 2]$ $\phantom{-}e$
11 $[11, 11, w - 1]$ $-\frac{1}{5}e^{2} - \frac{1}{5}e - \frac{12}{5}$
19 $[19, 19, w^{3} - w^{2} - 4w]$ $\phantom{-}\frac{7}{5}e^{3} + 2e^{2} - \frac{68}{5}e - \frac{24}{5}$
19 $[19, 19, -w^{5} + 2w^{4} + 6w^{3} - 7w^{2} - 10w + 1]$ $-e^{3} - \frac{8}{5}e^{2} + \frac{47}{5}e + \frac{24}{5}$
29 $[29, 29, w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 3w - 3]$ $-\frac{7}{5}e^{3} - \frac{8}{5}e^{2} + 15e + \frac{33}{5}$
29 $[29, 29, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 6w - 2]$ $\phantom{-}1$
29 $[29, 29, w^{5} - 3w^{4} - 2w^{3} + 6w^{2} + 2w + 1]$ $\phantom{-}\frac{6}{5}e^{3} + \frac{8}{5}e^{2} - \frac{61}{5}e - \frac{31}{5}$
29 $[29, 29, -w^{4} + 4w^{3} - 9w]$ $\phantom{-}\frac{1}{5}e^{3} + \frac{4}{5}e^{2} - e - \frac{9}{5}$
31 $[31, 31, w^{4} - 3w^{3} - 2w^{2} + 6w + 1]$ $\phantom{-}\frac{2}{5}e^{2} - \frac{8}{5}e - \frac{26}{5}$
41 $[41, 41, -2w^{5} + 6w^{4} + 5w^{3} - 15w^{2} - 6w + 3]$ $-\frac{6}{5}e^{3} - \frac{7}{5}e^{2} + \frac{62}{5}e + \frac{23}{5}$
59 $[59, 59, -2w^{5} + 6w^{4} + 6w^{3} - 16w^{2} - 11w + 1]$ $\phantom{-}\frac{3}{5}e^{3} + \frac{6}{5}e^{2} - \frac{26}{5}e - \frac{39}{5}$
61 $[61, 61, -2w^{5} + 6w^{4} + 5w^{3} - 14w^{2} - 7w]$ $-\frac{8}{5}e^{3} - \frac{11}{5}e^{2} + \frac{66}{5}e + \frac{24}{5}$
61 $[61, 61, 2w^{5} - 5w^{4} - 8w^{3} + 13w^{2} + 13w + 1]$ $-\frac{1}{5}e^{3} - \frac{1}{5}e^{2} + \frac{23}{5}e - 1$
61 $[61, 61, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w - 1]$ $\phantom{-}\frac{1}{5}e^{3} + \frac{1}{5}e^{2} - \frac{13}{5}e - 6$
61 $[61, 61, w^{3} - 2w^{2} - 3w - 1]$ $\phantom{-}\frac{12}{5}e^{3} + \frac{16}{5}e^{2} - \frac{137}{5}e - \frac{77}{5}$
64 $[64, 2, -2]$ $-\frac{3}{5}e^{3} + \frac{52}{5}e - \frac{4}{5}$
79 $[79, 79, -3w^{5} + 9w^{4} + 7w^{3} - 21w^{2} - 9w + 2]$ $-\frac{11}{5}e^{3} - \frac{23}{5}e^{2} + \frac{116}{5}e + \frac{86}{5}$
89 $[89, 89, w^{5} - 3w^{4} - 2w^{3} + 6w^{2} + 3w + 3]$ $-\frac{4}{5}e^{3} - 2e^{2} + \frac{41}{5}e + \frac{48}{5}$
101 $[101, 101, -w^{5} + 4w^{4} - w^{3} - 8w^{2} + 5w]$ $-\frac{4}{5}e^{3} - \frac{8}{5}e^{2} + \frac{58}{5}e + \frac{17}{5}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$29$ $[29, 29, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 6w - 2]$ $-1$