# Properties

 Label 4.4.4525.1-41.2-a Base field 4.4.4525.1 Weight $[2, 2, 2, 2]$ Level norm $41$ Level $[41,41,\frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{7}{3}w + 3]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

# Learn more about

## Base field 4.4.4525.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 7x^{2} + 3x + 9$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[41,41,\frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{7}{3}w + 3]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $11$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} + 2x^{3} - 15x^{2} - 28x - 5$$
Norm Prime Eigenvalue
5 $[5, 5, -\frac{1}{3}w^{3} - \frac{2}{3}w^{2} + \frac{7}{3}w + 4]$ $\phantom{-}\frac{1}{6}e^{3} - 3e - \frac{13}{6}$
5 $[5, 5, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{1}{3}w + 3]$ $\phantom{-}e$
9 $[9, 3, -w]$ $-e - 1$
9 $[9, 3, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{7}{3}w + 1]$ $-\frac{1}{3}e^{3} - \frac{1}{2}e^{2} + \frac{11}{2}e + \frac{29}{6}$
16 $[16, 2, 2]$ $-\frac{1}{3}e^{3} + 4e - \frac{5}{3}$
19 $[19, 19, \frac{2}{3}w^{3} - \frac{2}{3}w^{2} - \frac{11}{3}w]$ $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - \frac{15}{2}e - 7$
19 $[19, 19, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{1}{3}w + 1]$ $\phantom{-}\frac{1}{3}e^{3} - 5e - \frac{10}{3}$
31 $[31, 31, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{11}{3}w - 2]$ $\phantom{-}\frac{1}{6}e^{3} + \frac{1}{2}e^{2} - \frac{5}{2}e - \frac{17}{3}$
31 $[31, 31, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{5}{3}w + 5]$ $-\frac{2}{3}e^{3} - \frac{1}{2}e^{2} + \frac{19}{2}e + \frac{31}{6}$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 6]$ $\phantom{-}\frac{1}{2}e^{2} + \frac{1}{2}e - \frac{9}{2}$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 3]$ $\phantom{-}1$
61 $[61, 61, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} + \frac{2}{3}w + 4]$ $\phantom{-}\frac{1}{6}e^{3} - e + \frac{47}{6}$
61 $[61, 61, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{14}{3}w - 2]$ $\phantom{-}\frac{1}{6}e^{3} + \frac{1}{2}e^{2} - \frac{3}{2}e - \frac{29}{3}$
71 $[71, 71, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{1}{3}w - 7]$ $-\frac{1}{6}e^{3} - e^{2} + 2e + \frac{13}{6}$
71 $[71, 71, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - \frac{7}{3}w]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{13}{2}e + 2$
89 $[89, 89, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{10}{3}w - 3]$ $\phantom{-}\frac{2}{3}e^{3} + e^{2} - 9e - \frac{44}{3}$
89 $[89, 89, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w - 1]$ $-\frac{3}{2}e^{3} - e^{2} + 23e + \frac{37}{2}$
101 $[101, 101, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{7}{3}w - 3]$ $\phantom{-}\frac{5}{6}e^{3} + e^{2} - 10e - \frac{53}{6}$
101 $[101, 101, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + \frac{11}{3}w - 4]$ $\phantom{-}\frac{1}{2}e^{2} + \frac{3}{2}e - \frac{23}{2}$
101 $[101, 101, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{8}{3}w + 3]$ $-\frac{1}{2}e^{3} - e^{2} + 5e + \frac{9}{2}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$41$ $[41,41,\frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{7}{3}w + 3]$ $-1$