Properties

Base field 6.6.485125.1
Weight [2, 2, 2, 2, 2, 2]
Level norm 41
Level $[41, 41, 2w^{5} - 2w^{4} - 10w^{3} + 7w^{2} + 11w - 4]$
Label 6.6.485125.1-41.1-c
Dimension 5
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 $[41, 41, 2w^{5} - 2w^{4} - 10w^{3} + 7w^{2} + 11w - 4]$
Label 6.6.485125.1-41.1-c
Dimension 5
Is CM no
Is base change no
Parent newspace dimension 7

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} + 2x^{4} - 24x^{3} - 20x^{2} + 48x - 8\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, -w^{2} + 2]$ $\phantom{-}e$
19 $[19, 19, -w^{3} + 4w]$ $\phantom{-}\frac{1}{6}e^{3} - \frac{10}{3}e + \frac{10}{3}$
19 $[19, 19, w^{3} - 3w - 1]$ $\phantom{-}\frac{1}{4}e^{4} + \frac{2}{3}e^{3} - \frac{11}{2}e^{2} - \frac{28}{3}e + \frac{22}{3}$
29 $[29, 29, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 8w - 3]$ $-\frac{1}{6}e^{4} - \frac{1}{2}e^{3} + \frac{10}{3}e^{2} + \frac{20}{3}e$
29 $[29, 29, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ $-\frac{1}{6}e^{4} - \frac{1}{2}e^{3} + \frac{10}{3}e^{2} + \frac{20}{3}e$
31 $[31, 31, -w^{4} + 4w^{2} + w - 3]$ $-\frac{1}{12}e^{4} - \frac{1}{3}e^{3} + \frac{5}{3}e^{2} + 6e + \frac{4}{3}$
41 $[41, 41, 2w^{5} - 2w^{4} - 10w^{3} + 7w^{2} + 11w - 4]$ $-1$
49 $[49, 7, -2w^{5} + 3w^{4} + 10w^{3} - 12w^{2} - 11w + 6]$ $\phantom{-}\frac{1}{12}e^{4} - \frac{13}{6}e^{2} + \frac{8}{3}e + 4$
59 $[59, 59, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 7w - 5]$ $-\frac{1}{2}e^{4} - \frac{4}{3}e^{3} + 11e^{2} + \frac{47}{3}e - \frac{32}{3}$
59 $[59, 59, w^{5} - w^{4} - 4w^{3} + 3w^{2} + 3w - 3]$ $\phantom{-}\frac{1}{2}e^{4} + \frac{7}{6}e^{3} - 11e^{2} - \frac{34}{3}e + \frac{34}{3}$
59 $[59, 59, 2w^{5} - 3w^{4} - 9w^{3} + 11w^{2} + 9w - 4]$ $-\frac{1}{12}e^{4} - \frac{1}{3}e^{3} + \frac{13}{6}e^{2} + 6e - \frac{20}{3}$
61 $[61, 61, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 7w + 1]$ $-\frac{1}{6}e^{4} - \frac{1}{3}e^{3} + \frac{10}{3}e^{2} + \frac{7}{3}e - \frac{8}{3}$
64 $[64, 2, -2]$ $\phantom{-}\frac{5}{12}e^{4} + \frac{2}{3}e^{3} - \frac{31}{3}e^{2} - 6e + \frac{49}{3}$
71 $[71, 71, -2w^{5} + 2w^{4} + 10w^{3} - 8w^{2} - 11w + 6]$ $-\frac{1}{3}e^{4} - e^{3} + \frac{20}{3}e^{2} + \frac{37}{3}e - 6$
79 $[79, 79, -3w^{5} + 4w^{4} + 13w^{3} - 14w^{2} - 9w + 5]$ $\phantom{-}\frac{1}{6}e^{4} + \frac{1}{6}e^{3} - \frac{13}{3}e^{2} - 2e + \frac{34}{3}$
79 $[79, 79, -w^{4} - w^{3} + 5w^{2} + 4w - 3]$ $\phantom{-}\frac{1}{12}e^{4} + \frac{1}{3}e^{3} - \frac{7}{6}e^{2} - 4e - \frac{4}{3}$
79 $[79, 79, -2w^{5} + 2w^{4} + 9w^{3} - 7w^{2} - 8w + 4]$ $-\frac{1}{12}e^{4} + \frac{13}{6}e^{2} - \frac{8}{3}e$
81 $[81, 3, 3w^{5} - 5w^{4} - 14w^{3} + 19w^{2} + 13w - 8]$ $-\frac{7}{12}e^{4} - \frac{3}{2}e^{3} + \frac{41}{3}e^{2} + \frac{58}{3}e - 20$
89 $[89, 89, 2w^{5} - 2w^{4} - 9w^{3} + 6w^{2} + 8w - 1]$ $\phantom{-}\frac{1}{3}e^{4} + \frac{5}{6}e^{3} - \frac{23}{3}e^{2} - 10e + \frac{44}{3}$
101 $[101, 101, -w^{4} - w^{3} + 5w^{2} + 3w - 3]$ $-\frac{7}{12}e^{4} - \frac{4}{3}e^{3} + \frac{41}{3}e^{2} + 16e - \frac{50}{3}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
41 $[41, 41, 2w^{5} - 2w^{4} - 10w^{3} + 7w^{2} + 11w - 4]$ $1$