# Properties

 Label 4.4.4525.1-41.1-b Base field 4.4.4525.1 Weight $[2, 2, 2, 2]$ Level norm $41$ Level $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 6]$ Dimension $7$ CM no Base change no

# Related objects

• L-function not available

## 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: $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 6]$ Dimension: $7$ 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:

 $$x^{7} - 4x^{6} - 17x^{5} + 80x^{4} + 29x^{3} - 386x^{2} + 396x - 72$$
Norm Prime Eigenvalue
5 $[5, 5, -\frac{1}{3}w^{3} - \frac{2}{3}w^{2} + \frac{7}{3}w + 4]$ $\phantom{-}e$
5 $[5, 5, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{1}{3}w + 3]$ $\phantom{-}\frac{1}{6}e^{6} - \frac{5}{12}e^{5} - \frac{43}{12}e^{4} + \frac{97}{12}e^{3} + \frac{113}{6}e^{2} - \frac{115}{3}e + 6$
9 $[9, 3, -w]$ $\phantom{-}\frac{1}{6}e^{6} - \frac{5}{12}e^{5} - \frac{10}{3}e^{4} + \frac{47}{6}e^{3} + \frac{193}{12}e^{2} - \frac{215}{6}e + 6$
9 $[9, 3, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{7}{3}w + 1]$ $-\frac{1}{3}e^{6} + \frac{5}{6}e^{5} + \frac{20}{3}e^{4} - \frac{47}{3}e^{3} - \frac{187}{6}e^{2} + \frac{215}{3}e - 18$
16 $[16, 2, 2]$ $-\frac{1}{12}e^{6} + \frac{1}{3}e^{5} + \frac{23}{12}e^{4} - \frac{20}{3}e^{3} - \frac{125}{12}e^{2} + \frac{95}{3}e - 8$
19 $[19, 19, \frac{2}{3}w^{3} - \frac{2}{3}w^{2} - \frac{11}{3}w]$ $-\frac{1}{12}e^{6} + \frac{1}{3}e^{5} + \frac{17}{12}e^{4} - \frac{17}{3}e^{3} - \frac{65}{12}e^{2} + \frac{133}{6}e - 4$
19 $[19, 19, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{1}{3}w + 1]$ $\phantom{-}\frac{1}{4}e^{6} - \frac{1}{2}e^{5} - 5e^{4} + \frac{39}{4}e^{3} + 23e^{2} - 46e + 14$
31 $[31, 31, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{11}{3}w - 2]$ $-\frac{1}{6}e^{6} + \frac{5}{12}e^{5} + \frac{10}{3}e^{4} - \frac{25}{3}e^{3} - \frac{187}{12}e^{2} + \frac{118}{3}e - 7$
31 $[31, 31, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{5}{3}w + 5]$ $-\frac{1}{4}e^{4} + \frac{1}{4}e^{3} + \frac{15}{4}e^{2} - \frac{3}{2}e - 6$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 6]$ $-1$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 3]$ $-\frac{1}{3}e^{6} + \frac{7}{12}e^{5} + \frac{43}{6}e^{4} - \frac{35}{3}e^{3} - \frac{455}{12}e^{2} + \frac{167}{3}e + 1$
61 $[61, 61, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} + \frac{2}{3}w + 4]$ $-\frac{1}{2}e^{6} + e^{5} + \frac{41}{4}e^{4} - \frac{83}{4}e^{3} - \frac{195}{4}e^{2} + \frac{215}{2}e - 30$
61 $[61, 61, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{14}{3}w - 2]$ $-\frac{1}{4}e^{5} + \frac{1}{4}e^{4} + \frac{11}{4}e^{3} - \frac{3}{2}e^{2} - 6$
71 $[71, 71, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{1}{3}w - 7]$ $\phantom{-}\frac{1}{2}e^{6} - \frac{3}{2}e^{5} - \frac{43}{4}e^{4} + \frac{113}{4}e^{3} + \frac{223}{4}e^{2} - \frac{251}{2}e + 24$
71 $[71, 71, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - \frac{7}{3}w]$ $-\frac{5}{12}e^{6} + \frac{11}{12}e^{5} + \frac{53}{6}e^{4} - \frac{211}{12}e^{3} - \frac{553}{12}e^{2} + \frac{244}{3}e - 3$
89 $[89, 89, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{10}{3}w - 3]$ $\phantom{-}\frac{5}{12}e^{6} - \frac{11}{12}e^{5} - \frac{25}{3}e^{4} + \frac{217}{12}e^{3} + \frac{463}{12}e^{2} - \frac{262}{3}e + 23$
89 $[89, 89, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w - 1]$ $-\frac{5}{6}e^{6} + \frac{11}{6}e^{5} + \frac{103}{6}e^{4} - \frac{107}{3}e^{3} - \frac{254}{3}e^{2} + \frac{503}{3}e - 24$
101 $[101, 101, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{7}{3}w - 3]$ $-\frac{7}{12}e^{6} + \frac{4}{3}e^{5} + \frac{38}{3}e^{4} - \frac{317}{12}e^{3} - \frac{397}{6}e^{2} + \frac{389}{3}e - 24$
101 $[101, 101, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + \frac{11}{3}w - 4]$ $\phantom{-}\frac{1}{12}e^{6} - \frac{1}{12}e^{5} - \frac{5}{3}e^{4} + \frac{35}{12}e^{3} + \frac{83}{12}e^{2} - \frac{133}{6}e + 12$
101 $[101, 101, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{8}{3}w + 3]$ $-\frac{1}{4}e^{5} - \frac{1}{2}e^{4} + \frac{9}{2}e^{3} + \frac{19}{4}e^{2} - \frac{33}{2}e + 12$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$41$ $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 6]$ $1$