# Properties

 Base field 4.4.9909.1 Weight [2, 2, 2, 2] Level norm 13 Level $[13, 13, -w^{3} + w^{2} + 3w - 1]$ Label 4.4.9909.1-13.1-c Dimension 6 CM no Base change no

# Related objects

• L-function not available

# Learn more about

## Base field 4.4.9909.1

Generator $$w$$, with minimal polynomial $$x^{4} - 6x^{2} - 3x + 3$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[13, 13, -w^{3} + w^{2} + 3w - 1]$ Label 4.4.9909.1-13.1-c Dimension 6 Is CM no Is base change no Parent newspace dimension 14

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{6} - 15x^{4} - 2x^{3} + 45x^{2} + 38x + 8$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
5 $[5, 5, w - 1]$ $-\frac{1}{2}e^{5} + \frac{15}{2}e^{3} - \frac{45}{2}e - 10$
7 $[7, 7, w^{3} - w^{2} - 4w + 1]$ $-\frac{1}{2}e^{5} + \frac{15}{2}e^{3} - \frac{45}{2}e - 10$
11 $[11, 11, -w^{2} + w + 2]$ $-\frac{3}{2}e^{5} + e^{4} + \frac{45}{2}e^{3} - 10e^{2} - \frac{133}{2}e - 26$
13 $[13, 13, -w^{3} + w^{2} + 3w - 1]$ $-1$
16 $[16, 2, 2]$ $\phantom{-}2e^{5} - e^{4} - 29e^{3} + 11e^{2} + 80e + 33$
17 $[17, 17, -w^{3} + 5w + 2]$ $-\frac{3}{2}e^{5} + e^{4} + \frac{43}{2}e^{3} - 12e^{2} - \frac{113}{2}e - 18$
29 $[29, 29, -w^{2} + w + 1]$ $-e^{2} - 2e + 8$
37 $[37, 37, -w^{3} + 2w^{2} + 4w - 4]$ $-\frac{1}{2}e^{5} + e^{4} + \frac{15}{2}e^{3} - 10e^{2} - \frac{39}{2}e - 4$
41 $[41, 41, -w^{3} + w^{2} + 5w + 1]$ $-\frac{3}{2}e^{5} + e^{4} + \frac{41}{2}e^{3} - 12e^{2} - \frac{95}{2}e - 14$
41 $[41, 41, w^{2} - 5]$ $\phantom{-}\frac{3}{2}e^{5} - e^{4} - \frac{41}{2}e^{3} + 12e^{2} + \frac{95}{2}e + 14$
47 $[47, 47, w^{3} - w^{2} - 5w - 2]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{15}{2}e^{3} + \frac{49}{2}e + 18$
47 $[47, 47, -w^{3} + 2w^{2} + 4w - 1]$ $\phantom{-}\frac{1}{2}e^{5} - e^{4} - \frac{15}{2}e^{3} + 12e^{2} + \frac{37}{2}e - 6$
53 $[53, 53, w^{3} - 4w - 4]$ $\phantom{-}2e^{3} + 2e^{2} - 19e - 12$
53 $[53, 53, 2w^{3} - 2w^{2} - 9w + 1]$ $-e^{3} + 7e - 4$
61 $[61, 61, -w^{3} + w^{2} + 6w - 2]$ $-e^{5} + 14e^{3} - 38e - 22$
71 $[71, 71, w^{3} - w^{2} - 6w - 2]$ $\phantom{-}e^{5} - 15e^{3} + 45e + 20$
103 $[103, 103, 2w^{3} - 2w^{2} - 8w + 1]$ $\phantom{-}e^{5} - 16e^{3} - 2e^{2} + 54e + 32$
103 $[103, 103, -3w^{3} + 3w^{2} + 13w - 5]$ $\phantom{-}2e^{5} - e^{4} - 28e^{3} + 12e^{2} + 70e + 24$
109 $[109, 109, 2w^{3} - w^{2} - 8w - 4]$ $-4e^{5} + 2e^{4} + 56e^{3} - 24e^{2} - 144e - 50$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
13 $[13, 13, -w^{3} + w^{2} + 3w - 1]$ $1$