# Properties

 Label 4.4.16225.1-25.1-g Base field 4.4.16225.1 Weight $[2, 2, 2, 2]$ Level norm $25$ Level $[25, 5, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{7}{3}w - 1]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

# Learn more about

## Base field 4.4.16225.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 13x^{2} + 6x + 36$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[25, 5, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{7}{3}w - 1]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $50$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} + 2x^{3} - 10x^{2} - 16x + 4$$
Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{4}{3}w + 6]$ $\phantom{-}e$
4 $[4, 2, -\frac{1}{3}w^{3} - \frac{2}{3}w^{2} + \frac{10}{3}w + 7]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - \frac{11}{3}e - \frac{8}{3}$
9 $[9, 3, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{7}{2}w - 9]$ $-e - 2$
9 $[9, 3, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - \frac{7}{3}w - 5]$ $-\frac{1}{3}e^{3} - \frac{1}{3}e^{2} + \frac{11}{3}e + \frac{2}{3}$
11 $[11, 11, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{1}{6}w]$ $\phantom{-}2$
19 $[19, 19, w + 1]$ $\phantom{-}\frac{1}{2}e^{3} + e^{2} - 5e - 4$
19 $[19, 19, \frac{1}{6}w^{3} - \frac{1}{6}w^{2} - \frac{13}{6}w + 2]$ $\phantom{-}\frac{1}{6}e^{3} - \frac{1}{3}e^{2} - \frac{1}{3}e + \frac{14}{3}$
25 $[25, 5, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{7}{3}w - 1]$ $\phantom{-}1$
29 $[29, 29, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{13}{6}w]$ $-\frac{1}{6}e^{3} - \frac{2}{3}e^{2} + \frac{1}{3}e + \frac{16}{3}$
29 $[29, 29, w - 1]$ $-\frac{1}{2}e^{3} + 5e + 2$
31 $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w + 3]$ $-\frac{5}{6}e^{3} - \frac{5}{6}e^{2} + \frac{26}{3}e + \frac{17}{3}$
31 $[31, 31, \frac{1}{6}w^{3} - \frac{1}{6}w^{2} - \frac{1}{6}w + 2]$ $-\frac{1}{6}e^{3} - \frac{1}{6}e^{2} - \frac{2}{3}e + \frac{1}{3}$
41 $[41, 41, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{9}{2}w + 5]$ $-\frac{1}{2}e^{3} - \frac{3}{2}e^{2} + 4e + 8$
41 $[41, 41, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 8]$ $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + 4e - 4$
59 $[59, 59, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w - 1]$ $-\frac{1}{6}e^{3} + \frac{1}{3}e^{2} + \frac{10}{3}e - \frac{20}{3}$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 7]$ $\phantom{-}\frac{1}{2}e^{3} - 6e - 6$
59 $[59, 59, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + 2]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - \frac{8}{3}e - \frac{8}{3}$
79 $[79, 79, w^{2} - 11]$ $-\frac{5}{6}e^{3} - \frac{4}{3}e^{2} + \frac{17}{3}e + \frac{26}{3}$
79 $[79, 79, \frac{1}{6}w^{3} - \frac{7}{6}w^{2} - \frac{7}{6}w + 3]$ $-\frac{7}{6}e^{3} - \frac{2}{3}e^{2} + \frac{31}{3}e + \frac{16}{3}$
89 $[89, 89, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{19}{6}w - 5]$ $-\frac{2}{3}e^{3} - \frac{5}{3}e^{2} + \frac{19}{3}e + \frac{16}{3}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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