# Properties

 Label 4.4.13525.1-25.3-e Base field 4.4.13525.1 Weight $[2, 2, 2, 2]$ Level norm $25$ Level $[25,5,-w + 1]$ Dimension $5$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.13525.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 12x^{2} + 8x + 29$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[25,5,-w + 1]$ Dimension: $5$ CM: no Base change: no Newspace dimension: $25$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{5} - x^{4} - 13x^{3} + 8x^{2} + 41x - 3$$
Norm Prime Eigenvalue
5 $[5, 5, -w + 2]$ $\phantom{-}e$
5 $[5, 5, -\frac{3}{5}w^{3} - w^{2} + \frac{26}{5}w + \frac{42}{5}]$ $\phantom{-}0$
9 $[9, 3, \frac{2}{5}w^{3} - \frac{19}{5}w - \frac{3}{5}]$ $-\frac{4}{5}e^{4} - \frac{7}{5}e^{3} + \frac{29}{5}e^{2} + \frac{59}{5}e + \frac{7}{5}$
9 $[9, 3, -\frac{1}{5}w^{3} + \frac{2}{5}w + \frac{4}{5}]$ $\phantom{-}\frac{3}{5}e^{4} + \frac{4}{5}e^{3} - \frac{23}{5}e^{2} - \frac{33}{5}e + \frac{11}{5}$
11 $[11, 11, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{28}{5}]$ $-e^{4} - 2e^{3} + 8e^{2} + 15e$
11 $[11, 11, \frac{1}{5}w^{3} - w^{2} - \frac{7}{5}w + \frac{36}{5}]$ $-\frac{2}{5}e^{4} - \frac{1}{5}e^{3} + \frac{12}{5}e^{2} + \frac{12}{5}e + \frac{21}{5}$
16 $[16, 2, 2]$ $-\frac{1}{5}e^{4} + \frac{2}{5}e^{3} + \frac{11}{5}e^{2} - \frac{9}{5}e - \frac{22}{5}$
29 $[29, 29, -w]$ $-e^{4} + 8e^{2} + e - 6$
29 $[29, 29, \frac{1}{5}w^{3} - \frac{12}{5}w + \frac{1}{5}]$ $\phantom{-}\frac{3}{5}e^{4} + \frac{9}{5}e^{3} - \frac{23}{5}e^{2} - \frac{68}{5}e + \frac{21}{5}$
41 $[41, 41, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{38}{5}]$ $\phantom{-}\frac{1}{5}e^{4} - \frac{7}{5}e^{3} - \frac{16}{5}e^{2} + \frac{44}{5}e + \frac{57}{5}$
41 $[41, 41, -w^{2} + 10]$ $\phantom{-}2e^{4} + e^{3} - 16e^{2} - 11e + 9$
41 $[41, 41, \frac{11}{5}w^{3} + 3w^{2} - \frac{102}{5}w - \frac{149}{5}]$ $\phantom{-}e^{3} - 2e^{2} - 7e + 12$
41 $[41, 41, -\frac{1}{5}w^{3} + w^{2} + \frac{7}{5}w - \frac{26}{5}]$ $\phantom{-}\frac{8}{5}e^{4} + \frac{19}{5}e^{3} - \frac{63}{5}e^{2} - \frac{143}{5}e - \frac{9}{5}$
49 $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{19}{5}]$ $-e^{3} + 9e + 2$
49 $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{44}{5}]$ $-\frac{2}{5}e^{4} - \frac{1}{5}e^{3} + \frac{22}{5}e^{2} + \frac{7}{5}e - \frac{34}{5}$
59 $[59, 59, -\frac{4}{5}w^{3} - w^{2} + \frac{33}{5}w + \frac{36}{5}]$ $-\frac{11}{5}e^{4} - \frac{28}{5}e^{3} + \frac{81}{5}e^{2} + \frac{216}{5}e + \frac{48}{5}$
59 $[59, 59, -2w^{3} - 3w^{2} + 17w + 26]$ $\phantom{-}\frac{7}{5}e^{4} + \frac{11}{5}e^{3} - \frac{67}{5}e^{2} - \frac{92}{5}e + \frac{69}{5}$
61 $[61, 61, -\frac{1}{5}w^{3} + w^{2} + \frac{12}{5}w - \frac{51}{5}]$ $\phantom{-}\frac{1}{5}e^{4} - \frac{7}{5}e^{3} - \frac{11}{5}e^{2} + \frac{69}{5}e + \frac{37}{5}$
61 $[61, 61, \frac{4}{5}w^{3} + w^{2} - \frac{28}{5}w - \frac{41}{5}]$ $-\frac{12}{5}e^{4} - \frac{11}{5}e^{3} + \frac{97}{5}e^{2} + \frac{87}{5}e - \frac{59}{5}$
71 $[71, 71, \frac{1}{5}w^{3} + w^{2} - \frac{7}{5}w - \frac{49}{5}]$ $-\frac{6}{5}e^{4} - \frac{3}{5}e^{3} + \frac{46}{5}e^{2} + \frac{41}{5}e + \frac{3}{5}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5,5,-\frac{1}{5}w^{3} + \frac{12}{5}w + \frac{9}{5}]$ $1$