Properties

Base field 6.6.485125.1
Weight [2, 2, 2, 2, 2, 2]
Level norm 61
Level $[61, 61, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 7w + 1]$
Label 6.6.485125.1-61.1-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 $[61, 61, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 7w + 1]$
Label 6.6.485125.1-61.1-a
Dimension 4
Is CM no
Is base change no
Parent newspace dimension 12

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 2x^{3} - 24x^{2} - 70x - 25\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, -w^{2} + 2]$ $\phantom{-}e$
19 $[19, 19, -w^{3} + 4w]$ $\phantom{-}\frac{3}{10}e^{3} - \frac{2}{5}e^{2} - \frac{67}{10}e - 4$
19 $[19, 19, w^{3} - 3w - 1]$ $-\frac{1}{10}e^{3} - \frac{1}{5}e^{2} + \frac{19}{10}e + 2$
29 $[29, 29, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 8w - 3]$ $-\frac{2}{5}e^{3} + \frac{7}{10}e^{2} + \frac{33}{5}e - \frac{9}{2}$
29 $[29, 29, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ $-\frac{1}{2}e^{3} + \frac{21}{2}e + 12$
31 $[31, 31, -w^{4} + 4w^{2} + w - 3]$ $\phantom{-}\frac{1}{10}e^{3} + \frac{1}{5}e^{2} - \frac{19}{10}e - 9$
41 $[41, 41, 2w^{5} - 2w^{4} - 10w^{3} + 7w^{2} + 11w - 4]$ $\phantom{-}\frac{3}{5}e^{3} - \frac{3}{10}e^{2} - \frac{67}{5}e - \frac{31}{2}$
49 $[49, 7, -2w^{5} + 3w^{4} + 10w^{3} - 12w^{2} - 11w + 6]$ $-\frac{3}{5}e^{3} + \frac{4}{5}e^{2} + \frac{62}{5}e + 3$
59 $[59, 59, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 7w - 5]$ $-\frac{1}{2}e^{3} + e^{2} + \frac{17}{2}e - 4$
59 $[59, 59, w^{5} - w^{4} - 4w^{3} + 3w^{2} + 3w - 3]$ $\phantom{-}\frac{2}{5}e^{3} - \frac{7}{10}e^{2} - \frac{28}{5}e + \frac{3}{2}$
59 $[59, 59, 2w^{5} - 3w^{4} - 9w^{3} + 11w^{2} + 9w - 4]$ $\phantom{-}\frac{3}{5}e^{3} - \frac{4}{5}e^{2} - \frac{62}{5}e - 9$
61 $[61, 61, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 7w + 1]$ $\phantom{-}1$
64 $[64, 2, -2]$ $-\frac{3}{10}e^{3} - \frac{1}{10}e^{2} + \frac{67}{10}e + \frac{3}{2}$
71 $[71, 71, -2w^{5} + 2w^{4} + 10w^{3} - 8w^{2} - 11w + 6]$ $-\frac{1}{2}e^{2} + e + \frac{5}{2}$
79 $[79, 79, -3w^{5} + 4w^{4} + 13w^{3} - 14w^{2} - 9w + 5]$ $\phantom{-}\frac{7}{10}e^{3} + \frac{2}{5}e^{2} - \frac{153}{10}e - 22$
79 $[79, 79, -w^{4} - w^{3} + 5w^{2} + 4w - 3]$ $\phantom{-}\frac{1}{5}e^{3} - \frac{1}{10}e^{2} - \frac{14}{5}e - \frac{25}{2}$
79 $[79, 79, -2w^{5} + 2w^{4} + 9w^{3} - 7w^{2} - 8w + 4]$ $\phantom{-}\frac{7}{10}e^{3} - \frac{3}{5}e^{2} - \frac{153}{10}e - 11$
81 $[81, 3, 3w^{5} - 5w^{4} - 14w^{3} + 19w^{2} + 13w - 8]$ $\phantom{-}\frac{7}{10}e^{3} - \frac{11}{10}e^{2} - \frac{153}{10}e - \frac{5}{2}$
89 $[89, 89, 2w^{5} - 2w^{4} - 9w^{3} + 6w^{2} + 8w - 1]$ $\phantom{-}\frac{1}{2}e^{3} + e^{2} - \frac{29}{2}e - 24$
101 $[101, 101, -w^{4} - w^{3} + 5w^{2} + 3w - 3]$ $-\frac{3}{5}e^{3} + \frac{9}{5}e^{2} + \frac{57}{5}e - 11$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
61 $[61, 61, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 7w + 1]$ $-1$