# Properties

 Label 4.4.19600.1-25.1-p Base field $$\Q(\sqrt{5}, \sqrt{7})$$ Weight $[2, 2, 2, 2]$ Level norm $25$ Level $[25, 5, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{40}{23}w - \frac{21}{23}]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field $$\Q(\sqrt{5}, \sqrt{7})$$

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 15x^{2} + 16x + 29$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[25, 5, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{40}{23}w - \frac{21}{23}]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $62$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} + 12x^{3} + 14x^{2} - 232x - 604$$
Norm Prime Eigenvalue
4 $[4, 2, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w + \frac{1}{23}]$ $-2$
9 $[9, 3, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w + \frac{24}{23}]$ $\phantom{-}\frac{1}{10}e^{3} + \frac{2}{5}e^{2} - \frac{14}{5}e - \frac{39}{5}$
9 $[9, 3, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w - \frac{68}{23}]$ $-\frac{1}{10}e^{3} - \frac{2}{5}e^{2} + \frac{14}{5}e + \frac{29}{5}$
19 $[19, 19, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w + \frac{24}{23}]$ $\phantom{-}e$
19 $[19, 19, -\frac{6}{23}w^{3} + \frac{9}{23}w^{2} + \frac{83}{23}w - \frac{20}{23}]$ $-\frac{4}{15}e^{3} - \frac{26}{15}e^{2} + \frac{29}{5}e + \frac{532}{15}$
19 $[19, 19, \frac{6}{23}w^{3} - \frac{9}{23}w^{2} - \frac{83}{23}w + \frac{66}{23}]$ $\phantom{-}\frac{1}{10}e^{3} + \frac{2}{5}e^{2} - \frac{9}{5}e - \frac{4}{5}$
19 $[19, 19, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w - \frac{22}{23}]$ $-\frac{1}{6}e^{3} - \frac{4}{3}e^{2} + 3e + \frac{68}{3}$
25 $[25, 5, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{40}{23}w - \frac{21}{23}]$ $\phantom{-}1$
29 $[29, 29, w]$ $\phantom{-}\frac{1}{30}e^{3} + \frac{1}{15}e^{2} - 2e - \frac{83}{15}$
29 $[29, 29, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{63}{23}w - \frac{21}{23}]$ $\phantom{-}\frac{1}{6}e^{3} + \frac{11}{15}e^{2} - \frac{18}{5}e - \frac{181}{15}$
29 $[29, 29, \frac{4}{23}w^{3} - \frac{6}{23}w^{2} - \frac{63}{23}w + \frac{44}{23}]$ $-\frac{3}{10}e^{3} - \frac{9}{5}e^{2} + \frac{34}{5}e + 31$
29 $[29, 29, -w + 1]$ $\phantom{-}\frac{1}{10}e^{3} + e^{2} - \frac{6}{5}e - \frac{107}{5}$
31 $[31, 31, w + 2]$ $\phantom{-}\frac{3}{10}e^{3} + \frac{11}{5}e^{2} - \frac{27}{5}e - \frac{192}{5}$
31 $[31, 31, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{63}{23}w + \frac{25}{23}]$ $\phantom{-}\frac{2}{5}e^{3} + \frac{13}{5}e^{2} - \frac{41}{5}e - \frac{246}{5}$
31 $[31, 31, \frac{4}{23}w^{3} - \frac{6}{23}w^{2} - \frac{63}{23}w + \frac{90}{23}]$ $-\frac{7}{30}e^{3} - \frac{19}{15}e^{2} + \frac{21}{5}e + \frac{248}{15}$
31 $[31, 31, -w + 3]$ $-\frac{2}{15}e^{3} - \frac{13}{15}e^{2} + \frac{7}{5}e + \frac{206}{15}$
49 $[49, 7, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w - \frac{22}{23}]$ $\phantom{-}6$
59 $[59, 59, -\frac{20}{23}w^{3} + \frac{30}{23}w^{2} + \frac{269}{23}w - \frac{128}{23}]$ $\phantom{-}\frac{3}{10}e^{3} + 2e^{2} - \frac{28}{5}e - \frac{216}{5}$
59 $[59, 59, -\frac{8}{23}w^{3} + \frac{12}{23}w^{2} + \frac{103}{23}w - \frac{88}{23}]$ $\phantom{-}\frac{3}{10}e^{3} + 2e^{2} - \frac{28}{5}e - \frac{136}{5}$
59 $[59, 59, -\frac{8}{23}w^{3} + \frac{12}{23}w^{2} + \frac{103}{23}w - \frac{19}{23}]$ $-\frac{7}{30}e^{3} - \frac{22}{15}e^{2} + 4e + \frac{476}{15}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$25$ $[25,5,-\frac{4}{23}w^{3}+\frac{6}{23}w^{2}+\frac{40}{23}w-\frac{21}{23}]$ $-1$