# Properties

 Label 4.4.19525.1-25.2-i Base field 4.4.19525.1 Weight $[2, 2, 2, 2]$ Level norm $25$ Level $[25, 5, \frac{2}{3}w^{2} - \frac{2}{3}w - 5]$ Dimension $4$ CM no Base change yes

# Related objects

• L-function not available

## Base field 4.4.19525.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 14x^{2} + 15x + 45$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[25, 5, \frac{2}{3}w^{2} - \frac{2}{3}w - 5]$ Dimension: $4$ CM: no Base change: yes Newspace dimension: $46$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} + 9x^{3} + 18x^{2} - 19x - 40$$
Norm Prime Eigenvalue
5 $[5, 5, \frac{2}{3}w^{2} + \frac{1}{3}w - 5]$ $-1$
5 $[5, 5, \frac{2}{3}w^{2} - \frac{5}{3}w - 4]$ $-1$
9 $[9, 3, -w + 3]$ $\phantom{-}e$
9 $[9, 3, w + 2]$ $\phantom{-}e$
11 $[11, 11, \frac{2}{3}w^{2} + \frac{1}{3}w - 4]$ $-4e^{3} - 18e^{2} + 8e + 32$
16 $[16, 2, 2]$ $-e^{3} - 4e^{2} + 4e + 13$
19 $[19, 19, \frac{1}{3}w^{3} - \frac{10}{3}w - 3]$ $-2e^{3} - 10e^{2} - e + 20$
19 $[19, 19, \frac{1}{3}w^{3} - w^{2} - \frac{7}{3}w + 6]$ $-2e^{3} - 10e^{2} - e + 20$
29 $[29, 29, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 2]$ $-3e^{3} - 14e^{2} + 5e + 30$
29 $[29, 29, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $-3e^{3} - 14e^{2} + 5e + 30$
31 $[31, 31, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w + 1]$ $\phantom{-}5e^{3} + 22e^{2} - 11e - 38$
31 $[31, 31, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 4]$ $\phantom{-}5e^{3} + 22e^{2} - 11e - 38$
49 $[49, 7, \frac{1}{3}w^{3} - \frac{10}{3}w - 1]$ $-7e^{3} - 31e^{2} + 19e + 70$
49 $[49, 7, -\frac{1}{3}w^{3} + w^{2} + \frac{7}{3}w - 4]$ $-7e^{3} - 31e^{2} + 19e + 70$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{5}{3}w - 11]$ $\phantom{-}11e^{3} + 49e^{2} - 24e - 90$
59 $[59, 59, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 5w - 13]$ $\phantom{-}11e^{3} + 49e^{2} - 24e - 90$
61 $[61, 61, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{2}{3}w - 9]$ $\phantom{-}8e^{3} + 37e^{2} - 16e - 82$
61 $[61, 61, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 4w + 2]$ $\phantom{-}2e^{2} + 7e - 2$
61 $[61, 61, \frac{2}{3}w^{2} - \frac{5}{3}w - 1]$ $\phantom{-}2e^{2} + 7e - 2$
61 $[61, 61, -\frac{1}{3}w^{2} + \frac{4}{3}w + 6]$ $\phantom{-}8e^{3} + 37e^{2} - 16e - 82$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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