Properties

Base field 6.6.485125.1
Weight [2, 2, 2, 2, 2, 2]
Level norm 29
Level $[29, 29, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 8w - 3]$
Label 6.6.485125.1-29.1-a
Dimension 4
CM no
Base change no

Related objects

Downloads

Learn more about

Base field 6.6.485125.1

Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 4x^{4} + 8x^{3} + 2x^{2} - 5x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2, 2, 2]
Level $[29, 29, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 8w - 3]$
Label 6.6.485125.1-29.1-a
Dimension 4
Is CM no
Is base change no
Parent newspace dimension 4

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 2x^{3} - 27x^{2} + 40x + 145\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, -w^{2} + 2]$ $\phantom{-}e$
19 $[19, 19, -w^{3} + 4w]$ $-\frac{4}{3}e^{3} - 3e^{2} + 24e + \frac{152}{3}$
19 $[19, 19, w^{3} - 3w - 1]$ $\phantom{-}\frac{2}{3}e^{3} + e^{2} - 12e - \frac{43}{3}$
29 $[29, 29, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 8w - 3]$ $-1$
29 $[29, 29, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ $\phantom{-}\frac{5}{3}e^{3} + 4e^{2} - 31e - \frac{190}{3}$
31 $[31, 31, -w^{4} + 4w^{2} + w - 3]$ $-e^{3} - 2e^{2} + 19e + 30$
41 $[41, 41, 2w^{5} - 2w^{4} - 10w^{3} + 7w^{2} + 11w - 4]$ $\phantom{-}\frac{2}{3}e^{3} + 2e^{2} - 12e - \frac{94}{3}$
49 $[49, 7, -2w^{5} + 3w^{4} + 10w^{3} - 12w^{2} - 11w + 6]$ $-\frac{2}{3}e^{3} - 2e^{2} + 12e + \frac{106}{3}$
59 $[59, 59, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 7w - 5]$ $-\frac{2}{3}e^{3} + 12e + \frac{16}{3}$
59 $[59, 59, w^{5} - w^{4} - 4w^{3} + 3w^{2} + 3w - 3]$ $\phantom{-}\frac{2}{3}e^{3} + e^{2} - 12e - \frac{55}{3}$
59 $[59, 59, 2w^{5} - 3w^{4} - 9w^{3} + 11w^{2} + 9w - 4]$ $-\frac{2}{3}e^{3} + 12e + \frac{16}{3}$
61 $[61, 61, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 7w + 1]$ $-\frac{4}{3}e^{3} - 4e^{2} + 24e + \frac{182}{3}$
64 $[64, 2, -2]$ $-\frac{1}{3}e^{3} + 4e + \frac{8}{3}$
71 $[71, 71, -2w^{5} + 2w^{4} + 10w^{3} - 8w^{2} - 11w + 6]$ $\phantom{-}\frac{10}{3}e^{3} + 7e^{2} - 60e - \frac{335}{3}$
79 $[79, 79, -3w^{5} + 4w^{4} + 13w^{3} - 14w^{2} - 9w + 5]$ $-\frac{8}{3}e^{3} - 6e^{2} + 48e + \frac{292}{3}$
79 $[79, 79, -w^{4} - w^{3} + 5w^{2} + 4w - 3]$ $\phantom{-}e^{2} - 2e - 16$
79 $[79, 79, -2w^{5} + 2w^{4} + 9w^{3} - 7w^{2} - 8w + 4]$ $\phantom{-}\frac{4}{3}e^{3} + 2e^{2} - 22e - \frac{92}{3}$
81 $[81, 3, 3w^{5} - 5w^{4} - 14w^{3} + 19w^{2} + 13w - 8]$ $-2e^{3} - 4e^{2} + 34e + 68$
89 $[89, 89, 2w^{5} - 2w^{4} - 9w^{3} + 6w^{2} + 8w - 1]$ $\phantom{-}e^{2} - 2e - 12$
101 $[101, 101, -w^{4} - w^{3} + 5w^{2} + 3w - 3]$ $\phantom{-}2e^{3} + 4e^{2} - 36e - 62$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
29 $[29, 29, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 8w - 3]$ $1$