# Properties

 Label 4.4.10025.1-20.3-d Base field 4.4.10025.1 Weight $[2, 2, 2, 2]$ Level norm $20$ Level $[20,10,-w - 2]$ Dimension $5$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.10025.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 11x^{2} + 10x + 20$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[20,10,-w - 2]$ Dimension: $5$ CM: no Base change: no Newspace dimension: $13$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{5} - 2x^{4} - 13x^{3} + 12x^{2} + 48x + 16$$
Norm Prime Eigenvalue
4 $[4, 2, -w + 2]$ $\phantom{-}1$
4 $[4, 2, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 4]$ $\phantom{-}e$
5 $[5, 5, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{7}{2}w + 10]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{9}{2}e - 3$
5 $[5, 5, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{5}{2}w + 3]$ $\phantom{-}1$
19 $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 3]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{2}e^{3} - \frac{13}{4}e^{2} + 3e + 8$
19 $[19, 19, w - 1]$ $-\frac{1}{4}e^{4} - \frac{1}{2}e^{3} + \frac{13}{4}e^{2} + 4e - 2$
31 $[31, 31, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{7}{2}w - 6]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{2}e^{3} - \frac{13}{4}e^{2} + 5e + 10$
31 $[31, 31, -w^{3} - 2w^{2} + 7w + 13]$ $-\frac{1}{2}e^{4} + \frac{3}{2}e^{3} + \frac{5}{2}e^{2} - \frac{13}{2}e + 3$
49 $[49, 7, -2w^{3} - 2w^{2} + 15w + 9]$ $-\frac{1}{4}e^{4} + \frac{1}{2}e^{3} + \frac{17}{4}e^{2} - 5e - 15$
49 $[49, 7, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{9}{2}w - 4]$ $\phantom{-}e^{4} - 3e^{3} - 7e^{2} + 17e + 14$
59 $[59, 59, -\frac{3}{2}w^{3} - \frac{3}{2}w^{2} + \frac{17}{2}w + 8]$ $\phantom{-}\frac{5}{4}e^{4} - \frac{7}{2}e^{3} - \frac{41}{4}e^{2} + 18e + 22$
59 $[59, 59, -\frac{1}{2}w^{3} - \frac{5}{2}w^{2} + \frac{11}{2}w + 9]$ $-e^{3} + e^{2} + 7e + 1$
61 $[61, 61, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{9}{2}w + 9]$ $-\frac{1}{2}e^{4} + \frac{5}{2}e^{3} + \frac{9}{2}e^{2} - \frac{39}{2}e - 15$
61 $[61, 61, -\frac{3}{2}w^{3} - \frac{5}{2}w^{2} + \frac{23}{2}w + 12]$ $-\frac{1}{4}e^{4} + \frac{3}{2}e^{3} - \frac{3}{4}e^{2} - 8e + 12$
71 $[71, 71, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{23}{2}w - 1]$ $-\frac{3}{4}e^{4} + \frac{1}{2}e^{3} + \frac{31}{4}e^{2} - 10$
71 $[71, 71, \frac{3}{2}w^{3} + \frac{3}{2}w^{2} - \frac{19}{2}w - 9]$ $-\frac{1}{4}e^{4} + \frac{3}{2}e^{3} + \frac{5}{4}e^{2} - 12e - 8$
79 $[79, 79, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{11}{2}w + 4]$ $-\frac{1}{4}e^{4} + \frac{13}{4}e^{2} - \frac{5}{2}e - 3$
79 $[79, 79, -\frac{5}{2}w^{3} - \frac{7}{2}w^{2} + \frac{37}{2}w + 18]$ $\phantom{-}2e^{3} - e^{2} - 16e - 3$
81 $[81, 3, -3]$ $\phantom{-}\frac{3}{4}e^{4} - \frac{5}{2}e^{3} - \frac{31}{4}e^{2} + 16e + 24$
89 $[89, 89, w^{3} - 7w + 1]$ $-\frac{3}{4}e^{4} + \frac{3}{2}e^{3} + \frac{15}{4}e^{2} - 5e + 8$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4,2,w - 2]$ $-1$
$5$ $[5,5,w^{3} + 2w^{2} - 7w - 9]$ $-1$