# Properties

 Base field 4.4.11525.1 Weight [2, 2, 2, 2] Level norm 25 Level $[25,5,\frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 1]$ Label 4.4.11525.1-25.3-c Dimension 4 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.11525.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 11x^{2} + 5x + 25$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[25,5,\frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 1]$ Label 4.4.11525.1-25.3-c Dimension 4 Is CM no Is base change no Parent newspace dimension 20

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4}$$ $$\mathstrut +\mathstrut x^{3}$$ $$\mathstrut -\mathstrut 14x^{2}$$ $$\mathstrut -\mathstrut x$$ $$\mathstrut +\mathstrut 33$$
Norm Prime Eigenvalue
5 $[5, 5, \frac{1}{5}w^{3} + \frac{4}{5}w^{2} - \frac{11}{5}w - 7]$ $\phantom{-}e$
5 $[5, 5, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ $\phantom{-}0$
11 $[11, 11, w + 1]$ $-\frac{1}{2}e^{3} - e^{2} + 4e + \frac{9}{2}$
11 $[11, 11, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 2]$ $-\frac{1}{2}e^{3} - e^{2} + 4e + \frac{9}{2}$
16 $[16, 2, 2]$ $-\frac{1}{2}e^{3} - e^{2} + 4e - \frac{1}{2}$
19 $[19, 19, -\frac{1}{5}w^{3} + \frac{1}{5}w^{2} + \frac{1}{5}w + 1]$ $-\frac{1}{2}e^{3} - 2e^{2} + 3e + \frac{19}{2}$
19 $[19, 19, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w]$ $\phantom{-}\frac{1}{2}e^{3} + 2e^{2} - 3e - \frac{19}{2}$
19 $[19, 19, -\frac{2}{5}w^{3} + \frac{2}{5}w^{2} + \frac{17}{5}w]$ $\phantom{-}\frac{1}{2}e^{3} + 2e^{2} - 3e - \frac{19}{2}$
19 $[19, 19, w - 1]$ $-\frac{1}{2}e^{3} - 2e^{2} + 3e + \frac{19}{2}$
29 $[29, 29, w^{2} - w - 8]$ $-e^{2} + 6$
29 $[29, 29, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{7}{5}w + 2]$ $\phantom{-}e^{2} - 6$
31 $[31, 31, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{1}{5}w + 2]$ $\phantom{-}e^{2} + e - 5$
31 $[31, 31, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{17}{5}w + 3]$ $\phantom{-}e^{2} + e - 5$
61 $[61, 61, -\frac{2}{5}w^{3} - \frac{3}{5}w^{2} + \frac{12}{5}w + 5]$ $\phantom{-}e + 1$
61 $[61, 61, -\frac{4}{5}w^{3} - \frac{6}{5}w^{2} + \frac{39}{5}w + 15]$ $\phantom{-}e + 1$
61 $[61, 61, \frac{3}{5}w^{3} + \frac{2}{5}w^{2} - \frac{18}{5}w - 3]$ $-\frac{1}{2}e^{3} - e^{2} + 5e + \frac{7}{2}$
61 $[61, 61, \frac{7}{5}w^{3} + \frac{3}{5}w^{2} - \frac{62}{5}w - 13]$ $-\frac{1}{2}e^{3} - e^{2} + 5e + \frac{7}{2}$
71 $[71, 71, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{6}{5}w + 4]$ $\phantom{-}2e^{2} + 2e - 12$
71 $[71, 71, w^{2} - 8]$ $\phantom{-}2e^{2} + 2e - 12$
79 $[79, 79, \frac{3}{5}w^{3} + \frac{12}{5}w^{2} - \frac{33}{5}w - 22]$ $\phantom{-}\frac{1}{2}e^{3} - 3e + \frac{5}{2}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
5 $[5,5,\frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ $1$