# Properties

 Label 4.4.5725.1-25.1-c Base field 4.4.5725.1 Weight $[2, 2, 2, 2]$ Level norm $25$ Level $[25, 5, \frac{2}{3}w^{3} - \frac{10}{3}w - \frac{1}{3}]$ Dimension $7$ CM no Base change yes

# Related objects

• L-function not available

## Base field 4.4.5725.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 8x^{2} + 6x + 11$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[25, 5, \frac{2}{3}w^{3} - \frac{10}{3}w - \frac{1}{3}]$ Dimension: $7$ CM: no Base change: yes Newspace dimension: $9$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{7} - 35x^{5} - 2x^{4} + 360x^{3} - 104x^{2} - 1184x + 896$$
Norm Prime Eigenvalue
9 $[9, 3, \frac{1}{3}w^{3} - \frac{8}{3}w - \frac{2}{3}]$ $\phantom{-}e$
9 $[9, 3, -w + 1]$ $\phantom{-}e$
11 $[11, 11, w]$ $-\frac{1}{2}e^{2} + \frac{1}{2}e + 5$
11 $[11, 11, -\frac{1}{3}w^{3} + \frac{2}{3}w + \frac{5}{3}]$ $\phantom{-}\frac{1}{8}e^{5} - \frac{1}{4}e^{4} - \frac{23}{8}e^{3} + 4e^{2} + \frac{27}{2}e - 17$
11 $[11, 11, \frac{1}{3}w^{3} - \frac{8}{3}w + \frac{1}{3}]$ $-\frac{1}{2}e^{2} + \frac{1}{2}e + 5$
11 $[11, 11, -\frac{2}{3}w^{3} + \frac{13}{3}w + \frac{4}{3}]$ $\phantom{-}\frac{1}{8}e^{5} - \frac{1}{4}e^{4} - \frac{23}{8}e^{3} + 4e^{2} + \frac{27}{2}e - 17$
16 $[16, 2, 2]$ $\phantom{-}\frac{1}{32}e^{6} - \frac{1}{8}e^{5} - \frac{19}{32}e^{4} + \frac{45}{16}e^{3} + \frac{1}{2}e^{2} - \frac{65}{4}e + 20$
25 $[25, 5, \frac{2}{3}w^{3} - \frac{10}{3}w - \frac{1}{3}]$ $-1$
29 $[29, 29, -w - 3]$ $-\frac{1}{16}e^{6} + \frac{27}{16}e^{4} + \frac{9}{8}e^{3} - 11e^{2} - \frac{17}{2}e + 20$
29 $[29, 29, -\frac{1}{3}w^{3} + \frac{8}{3}w - \frac{10}{3}]$ $-\frac{1}{16}e^{6} + \frac{27}{16}e^{4} + \frac{9}{8}e^{3} - 11e^{2} - \frac{17}{2}e + 20$
31 $[31, 31, w^{3} - 6w + 1]$ $\phantom{-}\frac{1}{16}e^{6} - \frac{1}{4}e^{5} - \frac{23}{16}e^{4} + \frac{45}{8}e^{3} + \frac{25}{4}e^{2} - \frac{61}{2}e + 17$
31 $[31, 31, w^{3} - 6w - 2]$ $\phantom{-}\frac{1}{16}e^{6} - \frac{1}{4}e^{5} - \frac{23}{16}e^{4} + \frac{45}{8}e^{3} + \frac{25}{4}e^{2} - \frac{61}{2}e + 17$
41 $[41, 41, \frac{2}{3}w^{3} + w^{2} - \frac{13}{3}w - \frac{10}{3}]$ $\phantom{-}\frac{1}{4}e^{5} - \frac{1}{4}e^{4} - \frac{25}{4}e^{3} + \frac{13}{4}e^{2} + 31e - 21$
41 $[41, 41, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{5}{3}]$ $\phantom{-}\frac{1}{4}e^{5} - \frac{1}{4}e^{4} - \frac{25}{4}e^{3} + \frac{13}{4}e^{2} + 31e - 21$
59 $[59, 59, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{8}{3}]$ $-\frac{1}{8}e^{6} + \frac{27}{8}e^{4} + \frac{7}{4}e^{3} - \frac{41}{2}e^{2} - 9e + 24$
59 $[59, 59, w^{3} + w^{2} - 6w - 4]$ $-\frac{1}{8}e^{6} + \frac{27}{8}e^{4} + \frac{7}{4}e^{3} - \frac{41}{2}e^{2} - 9e + 24$
79 $[79, 79, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - \frac{19}{3}]$ $-\frac{1}{16}e^{6} + \frac{1}{4}e^{5} + \frac{27}{16}e^{4} - \frac{49}{8}e^{3} - 11e^{2} + \frac{67}{2}e - 4$
79 $[79, 79, \frac{1}{3}w^{3} + w^{2} - \frac{2}{3}w - \frac{17}{3}]$ $-\frac{1}{16}e^{6} + \frac{1}{4}e^{5} + \frac{27}{16}e^{4} - \frac{49}{8}e^{3} - 11e^{2} + \frac{67}{2}e - 4$
89 $[89, 89, \frac{4}{3}w^{3} - \frac{23}{3}w - \frac{5}{3}]$ $\phantom{-}\frac{1}{16}e^{6} - \frac{1}{2}e^{5} - \frac{19}{16}e^{4} + \frac{95}{8}e^{3} + 4e^{2} - \frac{121}{2}e + 28$
89 $[89, 89, \frac{1}{3}w^{3} + 2w^{2} - \frac{5}{3}w - \frac{32}{3}]$ $\phantom{-}\frac{1}{16}e^{6} - \frac{1}{2}e^{5} - \frac{19}{16}e^{4} + \frac{95}{8}e^{3} + 4e^{2} - \frac{121}{2}e + 28$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$25$ $[25, 5, \frac{2}{3}w^{3} - \frac{10}{3}w - \frac{1}{3}]$ $1$