# Properties

 Label 4.4.13525.1-25.1-h Base field 4.4.13525.1 Weight $[2, 2, 2, 2]$ Level norm $25$ Level $[25, 5, \frac{2}{5}w^{3} - \frac{14}{5}w - \frac{3}{5}]$ Dimension $6$ CM no Base change yes

# 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: $[25, 5, \frac{2}{5}w^{3} - \frac{14}{5}w - \frac{3}{5}]$ Dimension: $6$ CM: no Base change: yes Newspace dimension: $27$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{6} - 2x^{5} - 18x^{4} + 30x^{3} + 85x^{2} - 84x - 100$$
Norm Prime Eigenvalue
5 $[5, 5, -w + 2]$ $-1$
5 $[5, 5, -\frac{3}{5}w^{3} - w^{2} + \frac{26}{5}w + \frac{42}{5}]$ $-1$
9 $[9, 3, \frac{2}{5}w^{3} - \frac{19}{5}w - \frac{3}{5}]$ $\phantom{-}e$
9 $[9, 3, -\frac{1}{5}w^{3} + \frac{2}{5}w + \frac{4}{5}]$ $\phantom{-}e$
11 $[11, 11, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{28}{5}]$ $\phantom{-}\frac{1}{4}e^{5} + \frac{1}{4}e^{4} - \frac{15}{4}e^{3} - \frac{11}{4}e^{2} + 12e + 5$
11 $[11, 11, \frac{1}{5}w^{3} - w^{2} - \frac{7}{5}w + \frac{36}{5}]$ $\phantom{-}\frac{1}{4}e^{5} + \frac{1}{4}e^{4} - \frac{15}{4}e^{3} - \frac{11}{4}e^{2} + 12e + 5$
16 $[16, 2, 2]$ $\phantom{-}\frac{3}{4}e^{5} + \frac{5}{4}e^{4} - \frac{43}{4}e^{3} - \frac{63}{4}e^{2} + \frac{57}{2}e + 35$
29 $[29, 29, -w]$ $-\frac{1}{4}e^{5} - \frac{1}{4}e^{4} + \frac{11}{4}e^{3} + \frac{11}{4}e^{2} - 2e - 5$
29 $[29, 29, \frac{1}{5}w^{3} - \frac{12}{5}w + \frac{1}{5}]$ $-\frac{1}{4}e^{5} - \frac{1}{4}e^{4} + \frac{11}{4}e^{3} + \frac{11}{4}e^{2} - 2e - 5$
41 $[41, 41, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{38}{5}]$ $-\frac{1}{4}e^{5} - \frac{3}{4}e^{4} + \frac{11}{4}e^{3} + \frac{37}{4}e^{2} - 3e - 15$
41 $[41, 41, -w^{2} + 10]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{11}{2}e^{2} + 8$
41 $[41, 41, \frac{11}{5}w^{3} + 3w^{2} - \frac{102}{5}w - \frac{149}{5}]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{11}{2}e^{2} + 8$
41 $[41, 41, -\frac{1}{5}w^{3} + w^{2} + \frac{7}{5}w - \frac{26}{5}]$ $-\frac{1}{4}e^{5} - \frac{3}{4}e^{4} + \frac{11}{4}e^{3} + \frac{37}{4}e^{2} - 3e - 15$
49 $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{19}{5}]$ $-e^{5} - e^{4} + 14e^{3} + 12e^{2} - 35e - 20$
49 $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{44}{5}]$ $-e^{5} - e^{4} + 14e^{3} + 12e^{2} - 35e - 20$
59 $[59, 59, -\frac{4}{5}w^{3} - w^{2} + \frac{33}{5}w + \frac{36}{5}]$ $-\frac{1}{2}e^{5} - e^{4} + \frac{15}{2}e^{3} + 15e^{2} - 24e - 40$
59 $[59, 59, -2w^{3} - 3w^{2} + 17w + 26]$ $-\frac{1}{2}e^{5} - e^{4} + \frac{15}{2}e^{3} + 15e^{2} - 24e - 40$
61 $[61, 61, -\frac{1}{5}w^{3} + w^{2} + \frac{12}{5}w - \frac{51}{5}]$ $\phantom{-}\frac{5}{4}e^{5} + \frac{5}{4}e^{4} - \frac{71}{4}e^{3} - \frac{59}{4}e^{2} + 45e + 25$
61 $[61, 61, \frac{4}{5}w^{3} + w^{2} - \frac{28}{5}w - \frac{41}{5}]$ $\phantom{-}\frac{5}{4}e^{5} + \frac{5}{4}e^{4} - \frac{71}{4}e^{3} - \frac{59}{4}e^{2} + 45e + 25$
71 $[71, 71, \frac{1}{5}w^{3} + w^{2} - \frac{7}{5}w - \frac{49}{5}]$ $\phantom{-}e^{2} - 10$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, -w + 2]$ $1$
$5$ $[5, 5, -\frac{3}{5}w^{3} - w^{2} + \frac{26}{5}w + \frac{42}{5}]$ $1$