# Properties

 Label 4.4.13025.1-20.1-e Base field 4.4.13025.1 Weight $[2, 2, 2, 2]$ Level norm $20$ Level $[20, 10, \frac{1}{2}w^{3} - w^{2} - 4w + \frac{11}{2}]$ Dimension $6$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.13025.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 12x^{2} + 3x + 29$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[20, 10, \frac{1}{2}w^{3} - w^{2} - 4w + \frac{11}{2}]$ Dimension: $6$ CM: no Base change: no Newspace dimension: $19$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{6} - 2x^{5} - 13x^{4} + 16x^{3} + 41x^{2} - 22x - 25$$
Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{2}w^{3} - 2w^{2} - 2w + \frac{15}{2}]$ $\phantom{-}e$
4 $[4, 2, -w^{2} + w + 8]$ $-1$
5 $[5, 5, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} + \frac{1}{2}w - \frac{9}{4}]$ $-1$
5 $[5, 5, \frac{1}{2}w^{3} - w^{2} - 4w + \frac{9}{2}]$ $-\frac{1}{10}e^{5} + \frac{2}{5}e^{4} + e^{3} - \frac{18}{5}e^{2} - \frac{19}{10}e + 4$
19 $[19, 19, \frac{1}{4}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + \frac{21}{4}]$ $-e^{2} + 2e + 5$
19 $[19, 19, \frac{1}{4}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + \frac{41}{4}]$ $\phantom{-}\frac{1}{5}e^{5} - \frac{3}{10}e^{4} - 2e^{3} + \frac{6}{5}e^{2} + \frac{9}{5}e + \frac{5}{2}$
29 $[29, 29, w]$ $-2e$
29 $[29, 29, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{1}{2}w + \frac{1}{4}]$ $-\frac{1}{10}e^{5} + \frac{2}{5}e^{4} + e^{3} - \frac{23}{5}e^{2} - \frac{19}{10}e + 5$
29 $[29, 29, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + \frac{9}{4}]$ $-e^{2} + 5$
29 $[29, 29, -\frac{1}{2}w^{3} + w^{2} + 4w - \frac{5}{2}]$ $-\frac{1}{2}e^{4} + e^{3} + 5e^{2} - 5e - \frac{15}{2}$
41 $[41, 41, \frac{3}{4}w^{3} - \frac{5}{2}w^{2} - \frac{7}{2}w + \frac{47}{4}]$ $\phantom{-}\frac{1}{5}e^{5} - \frac{4}{5}e^{4} - e^{3} + \frac{26}{5}e^{2} - \frac{6}{5}e - 2$
41 $[41, 41, \frac{1}{4}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w - \frac{15}{4}]$ $\phantom{-}\frac{2}{5}e^{5} - \frac{3}{5}e^{4} - 5e^{3} + \frac{17}{5}e^{2} + \frac{63}{5}e - 2$
61 $[61, 61, -\frac{3}{2}w^{3} + 3w^{2} + 11w - \frac{21}{2}]$ $\phantom{-}\frac{2}{5}e^{5} - \frac{8}{5}e^{4} - 3e^{3} + \frac{67}{5}e^{2} + \frac{23}{5}e - 17$
61 $[61, 61, w^{3} - 2w^{2} - 4w + 6]$ $\phantom{-}\frac{1}{5}e^{5} + \frac{1}{5}e^{4} - 3e^{3} - \frac{24}{5}e^{2} + \frac{44}{5}e + 13$
79 $[79, 79, \frac{3}{4}w^{3} - \frac{5}{2}w^{2} - \frac{7}{2}w + \frac{27}{4}]$ $\phantom{-}\frac{1}{5}e^{5} + \frac{1}{5}e^{4} - 4e^{3} - \frac{9}{5}e^{2} + \frac{79}{5}e$
79 $[79, 79, \frac{1}{4}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w - \frac{35}{4}]$ $-\frac{1}{5}e^{5} - \frac{1}{5}e^{4} + 4e^{3} + \frac{14}{5}e^{2} - \frac{79}{5}e - 5$
81 $[81, 3, -3]$ $-\frac{1}{5}e^{5} + \frac{4}{5}e^{4} + 2e^{3} - \frac{41}{5}e^{2} - \frac{19}{5}e + 13$
89 $[89, 89, \frac{7}{4}w^{3} - \frac{11}{2}w^{2} - \frac{21}{2}w + \frac{119}{4}]$ $-\frac{1}{10}e^{5} + \frac{2}{5}e^{4} - \frac{13}{5}e^{2} + \frac{31}{10}e + 5$
89 $[89, 89, \frac{1}{4}w^{3} + \frac{3}{2}w^{2} - \frac{3}{2}w - \frac{23}{4}]$ $\phantom{-}\frac{1}{5}e^{5} - \frac{4}{5}e^{4} - e^{3} + \frac{31}{5}e^{2} - \frac{6}{5}e - 5$
109 $[109, 109, -\frac{1}{2}w^{3} + 3w^{2} + 2w - \frac{41}{2}]$ $\phantom{-}\frac{2}{5}e^{5} - \frac{3}{5}e^{4} - 6e^{3} + \frac{22}{5}e^{2} + \frac{118}{5}e - 5$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, -w^{2} + w + 8]$ $1$
$5$ $[5, 5, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} + \frac{1}{2}w - \frac{9}{4}]$ $1$