# Properties

 Base field 4.4.725.1 Weight [2, 2, 2, 2] Level norm 169 Level $[169, 13, -4w^{3} + 5w^{2} + 8w - 4]$ Label 4.4.725.1-169.1-a Dimension 3 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.725.1

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

## Form

 Weight [2, 2, 2, 2] Level $[169, 13, -4w^{3} + 5w^{2} + 8w - 4]$ Label 4.4.725.1-169.1-a Dimension 3 Is CM no Is base change no Parent newspace dimension 3

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{3}$$ $$\mathstrut +\mathstrut 2x^{2}$$ $$\mathstrut -\mathstrut 20x$$ $$\mathstrut -\mathstrut 8$$
Norm Prime Eigenvalue
11 $[11, 11, -w^{3} + 2w^{2} + w - 3]$ $\phantom{-}e$
11 $[11, 11, w^{3} - 3w]$ $-\frac{1}{2}e + 1$
16 $[16, 2, 2]$ $-\frac{1}{4}e^{2} - \frac{3}{2}e + 3$
19 $[19, 19, -w^{3} + 2w + 2]$ $-\frac{1}{4}e^{2} + 5$
19 $[19, 19, 2w^{3} - 3w^{2} - 4w + 2]$ $-\frac{1}{8}e^{2} - \frac{1}{2}e + \frac{3}{2}$
25 $[25, 5, 2w^{3} - 2w^{2} - 4w + 1]$ $\phantom{-}\frac{3}{4}e^{2} + e - 9$
29 $[29, 29, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}\frac{1}{4}e^{2} + e - 1$
31 $[31, 31, w^{3} - 4w + 1]$ $-\frac{1}{8}e^{2} + \frac{1}{2}e + \frac{3}{2}$
31 $[31, 31, -w^{2} + 2w + 3]$ $\phantom{-}\frac{1}{2}e^{2} - 6$
41 $[41, 41, 2w^{2} - w - 3]$ $-\frac{1}{4}e^{2} - e + 5$
41 $[41, 41, -w^{3} + 3w^{2} + w - 4]$ $-\frac{7}{8}e^{2} - \frac{1}{2}e + \frac{25}{2}$
49 $[49, 7, 2w^{3} - 3w^{2} - 5w + 2]$ $\phantom{-}\frac{1}{8}e^{2} + \frac{1}{2}e + \frac{1}{2}$
49 $[49, 7, w^{2} + w - 3]$ $\phantom{-}\frac{1}{8}e^{2} - \frac{3}{2}e - \frac{19}{2}$
61 $[61, 61, 2w^{3} - 3w^{2} - 4w]$ $\phantom{-}\frac{7}{8}e^{2} + \frac{7}{2}e - \frac{25}{2}$
61 $[61, 61, -3w^{3} + 4w^{2} + 7w - 3]$ $-\frac{1}{8}e^{2} + \frac{1}{2}e - \frac{5}{2}$
79 $[79, 79, 2w^{3} - 4w^{2} - 3w + 2]$ $\phantom{-}\frac{1}{2}e^{2} + \frac{1}{2}e - 15$
79 $[79, 79, w^{3} + w^{2} - 3w - 5]$ $\phantom{-}\frac{1}{4}e^{2} + 2e + 3$
81 $[81, 3, -3]$ $\phantom{-}\frac{1}{4}e^{2} + \frac{3}{2}e - 6$
89 $[89, 89, -3w^{3} + 4w^{2} + 5w - 3]$ $-e^{2} + e + 18$
89 $[89, 89, 3w^{3} - 2w^{2} - 7w]$ $-\frac{1}{4}e^{2} - \frac{1}{2}e - 4$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
169 $[169, 13, -4w^{3} + 5w^{2} + 8w - 4]$ $1$