# Properties

 Label 4.4.19225.1-25.1-d Base field 4.4.19225.1 Weight $[2, 2, 2, 2]$ Level norm $25$ Level $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.19225.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 15x^{2} + 2x + 44$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $63$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} + x^{3} - 15x^{2} - 6x + 36$$
Norm Prime Eigenvalue
4 $[4, 2, w + 2]$ $\phantom{-}e$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ $\phantom{-}\frac{1}{6}e^{3} + \frac{1}{6}e^{2} - \frac{5}{2}e - 1$
9 $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{5}{2}w + 17]$ $-\frac{1}{6}e^{3} - \frac{1}{6}e^{2} + \frac{5}{2}e + 2$
9 $[9, 3, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 28]$ $-e + 1$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 11]$ $\phantom{-}e + 1$
11 $[11, 11, -w - 3]$ $\phantom{-}\frac{1}{6}e^{3} + \frac{1}{6}e^{2} - \frac{5}{2}e$
25 $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ $-1$
29 $[29, 29, w + 1]$ $\phantom{-}\frac{1}{2}e^{3} + \frac{3}{2}e^{2} - \frac{11}{2}e - 6$
29 $[29, 29, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 9]$ $\phantom{-}\frac{1}{6}e^{3} - \frac{5}{6}e^{2} - \frac{1}{2}e + 11$
31 $[31, 31, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 16]$ $-\frac{1}{6}e^{3} - \frac{7}{6}e^{2} - \frac{1}{2}e + 12$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 5]$ $-\frac{1}{3}e^{3} + \frac{2}{3}e^{2} + 4e - 6$
31 $[31, 31, -w + 3]$ $-\frac{1}{3}e^{3} - \frac{4}{3}e^{2} + 2e + 9$
31 $[31, 31, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 29]$ $-\frac{1}{3}e^{3} + \frac{2}{3}e^{2} + 5e - 2$
59 $[59, 59, 2w^{2} - w - 13]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - 3e - 1$
59 $[59, 59, \frac{9}{2}w^{3} - \frac{31}{2}w^{2} - \frac{61}{2}w + 85]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - 3e - 1$
61 $[61, 61, 2w^{3} - 6w^{2} - 15w + 31]$ $-e^{2} - 2e + 10$
61 $[61, 61, -\frac{3}{2}w^{3} + \frac{11}{2}w^{2} + \frac{21}{2}w - 34]$ $-\frac{1}{6}e^{3} + \frac{5}{6}e^{2} + \frac{7}{2}e - 4$
71 $[71, 71, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 32]$ $-\frac{1}{6}e^{3} - \frac{1}{6}e^{2} + \frac{1}{2}e + 4$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 13]$ $-\frac{1}{3}e^{3} - \frac{1}{3}e^{2} + 4e + 5$
79 $[79, 79, -3w^{3} + 10w^{2} + 19w - 51]$ $\phantom{-}\frac{2}{3}e^{3} + \frac{2}{3}e^{2} - 7e + 1$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$25$ $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ $1$