# Properties

 Label 4.4.12400.1-25.1-e Base field 4.4.12400.1 Weight $[2, 2, 2, 2]$ Level norm $25$ Level $[25, 5, w^{2} - 6]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.12400.1

Generator $$w$$, with minimal polynomial $$x^{4} - 12x^{2} + 31$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[25, 5, w^{2} - 6]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $30$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} + 2x^{3} - 24x^{2} - 62x - 1$$
Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{7}{2}w + \frac{11}{2}]$ $-2$
5 $[5, 5, -\frac{1}{2}w^{3} + w^{2} + \frac{5}{2}w - 4]$ $-1$
5 $[5, 5, -\frac{1}{2}w^{2} - w + \frac{3}{2}]$ $\phantom{-}1$
9 $[9, 3, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - \frac{9}{2}]$ $\phantom{-}e$
9 $[9, 3, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{7}{2}w + \frac{9}{2}]$ $\phantom{-}\frac{1}{6}e^{3} + \frac{1}{6}e^{2} - \frac{25}{6}e - \frac{31}{6}$
19 $[19, 19, -\frac{1}{2}w^{2} + w + \frac{5}{2}]$ $-\frac{1}{12}e^{3} + \frac{5}{12}e^{2} + \frac{7}{12}e - \frac{83}{12}$
19 $[19, 19, \frac{1}{2}w^{2} + w - \frac{5}{2}]$ $-\frac{1}{4}e^{3} + \frac{1}{4}e^{2} + \frac{23}{4}e + \frac{17}{4}$
29 $[29, 29, -\frac{3}{2}w^{2} - w + \frac{17}{2}]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{1}{6}e^{2} - \frac{22}{3}e - \frac{41}{6}$
29 $[29, 29, -\frac{3}{2}w^{2} + w + \frac{17}{2}]$ $-\frac{1}{6}e^{3} + \frac{1}{3}e^{2} + \frac{13}{6}e - \frac{13}{3}$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{7}{2}w]$ $\phantom{-}\frac{1}{6}e^{3} - \frac{5}{6}e^{2} - \frac{19}{6}e + \frac{47}{6}$
59 $[59, 59, \frac{1}{2}w^{2} + w - \frac{11}{2}]$ $\phantom{-}\frac{1}{4}e^{3} + \frac{1}{4}e^{2} - \frac{19}{4}e - \frac{43}{4}$
59 $[59, 59, \frac{1}{2}w^{2} - w - \frac{11}{2}]$ $-\frac{1}{4}e^{3} - \frac{1}{4}e^{2} + \frac{19}{4}e + \frac{19}{4}$
61 $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 5]$ $-\frac{1}{4}e^{3} + \frac{1}{4}e^{2} + \frac{11}{4}e + \frac{5}{4}$
61 $[61, 61, \frac{1}{2}w^{3} + w^{2} - \frac{7}{2}w - 5]$ $-\frac{7}{12}e^{3} - \frac{1}{12}e^{2} + \frac{157}{12}e + \frac{139}{12}$
71 $[71, 71, -\frac{1}{2}w^{3} - 2w^{2} + \frac{11}{2}w + 13]$ $-\frac{1}{4}e^{3} - \frac{3}{4}e^{2} + \frac{19}{4}e + \frac{57}{4}$
71 $[71, 71, \frac{3}{2}w^{3} + 2w^{2} - \frac{23}{2}w - 18]$ $-\frac{1}{4}e^{3} - \frac{3}{4}e^{2} + \frac{19}{4}e + \frac{57}{4}$
79 $[79, 79, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - \frac{1}{2}]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - \frac{16}{3}e - \frac{31}{3}$
79 $[79, 79, -2w^{2} + w + 10]$ $-\frac{7}{12}e^{3} - \frac{1}{12}e^{2} + \frac{145}{12}e + \frac{115}{12}$
79 $[79, 79, 2w^{2} + w - 10]$ $\phantom{-}\frac{5}{12}e^{3} - \frac{1}{12}e^{2} - \frac{83}{12}e - \frac{101}{12}$
79 $[79, 79, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w + \frac{1}{2}]$ $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - \frac{21}{2}e - \frac{31}{2}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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