# Properties

 Label 4.4.13525.1-5.1-b Base field 4.4.13525.1 Weight $[2, 2, 2, 2]$ Level norm $5$ Level $[5, 5, -w + 2]$ Dimension $3$ 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: $[5, 5, -w + 2]$ Dimension: $3$ CM: no Base change: no Newspace dimension: $4$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{3} - 3x^{2} - 13x + 31$$
Norm Prime Eigenvalue
5 $[5, 5, -w + 2]$ $-1$
5 $[5, 5, -\frac{3}{5}w^{3} - w^{2} + \frac{26}{5}w + \frac{42}{5}]$ $\phantom{-}e$
9 $[9, 3, \frac{2}{5}w^{3} - \frac{19}{5}w - \frac{3}{5}]$ $\phantom{-}\frac{1}{4}e^{2} + e - \frac{17}{4}$
9 $[9, 3, -\frac{1}{5}w^{3} + \frac{2}{5}w + \frac{4}{5}]$ $-\frac{1}{4}e^{2} - \frac{1}{2}e + \frac{19}{4}$
11 $[11, 11, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{28}{5}]$ $\phantom{-}\frac{1}{4}e^{2} + e - \frac{17}{4}$
11 $[11, 11, \frac{1}{5}w^{3} - w^{2} - \frac{7}{5}w + \frac{36}{5}]$ $-\frac{1}{4}e^{2} - \frac{1}{2}e + \frac{19}{4}$
16 $[16, 2, 2]$ $\phantom{-}\frac{1}{4}e^{2} - \frac{21}{4}$
29 $[29, 29, -w]$ $-\frac{1}{2}e^{2} + e + \frac{3}{2}$
29 $[29, 29, \frac{1}{5}w^{3} - \frac{12}{5}w + \frac{1}{5}]$ $-\frac{1}{2}e^{2} + 2e + \frac{15}{2}$
41 $[41, 41, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{38}{5}]$ $-e^{2} + 11$
41 $[41, 41, -w^{2} + 10]$ $\phantom{-}\frac{1}{4}e^{2} - \frac{3}{2}e + \frac{5}{4}$
41 $[41, 41, \frac{11}{5}w^{3} + 3w^{2} - \frac{102}{5}w - \frac{149}{5}]$ $\phantom{-}\frac{1}{4}e^{2} - \frac{3}{2}e + \frac{5}{4}$
41 $[41, 41, -\frac{1}{5}w^{3} + w^{2} + \frac{7}{5}w - \frac{26}{5}]$ $\phantom{-}\frac{3}{4}e^{2} - \frac{3}{2}e - \frac{29}{4}$
49 $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{19}{5}]$ $-\frac{5}{4}e^{2} - \frac{1}{2}e + \frac{63}{4}$
49 $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{44}{5}]$ $-\frac{3}{4}e^{2} + e + \frac{27}{4}$
59 $[59, 59, -\frac{4}{5}w^{3} - w^{2} + \frac{33}{5}w + \frac{36}{5}]$ $-\frac{3}{2}e^{2} + e + \frac{25}{2}$
59 $[59, 59, -2w^{3} - 3w^{2} + 17w + 26]$ $\phantom{-}\frac{1}{4}e^{2} - \frac{1}{2}e - \frac{23}{4}$
61 $[61, 61, -\frac{1}{5}w^{3} + w^{2} + \frac{12}{5}w - \frac{51}{5}]$ $-\frac{5}{4}e^{2} - \frac{1}{2}e + \frac{63}{4}$
61 $[61, 61, \frac{4}{5}w^{3} + w^{2} - \frac{28}{5}w - \frac{41}{5}]$ $\phantom{-}\frac{1}{2}e^{2} - 2e - \frac{5}{2}$
71 $[71, 71, \frac{1}{5}w^{3} + w^{2} - \frac{7}{5}w - \frac{49}{5}]$ $\phantom{-}e + 11$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, -w + 2]$ $1$