# Properties

 Label 4.4.4525.1-61.1-a Base field 4.4.4525.1 Weight $[2, 2, 2, 2]$ Level norm $61$ Level $[61, 61, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} + \frac{2}{3}w + 4]$ Dimension $6$ 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: $[61, 61, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} + \frac{2}{3}w + 4]$ Dimension: $6$ CM: no Base change: no Newspace dimension: $18$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{6} + 2x^{5} - 15x^{4} - 40x^{3} - 20x^{2} + 12x + 7$$
Norm Prime Eigenvalue
5 $[5, 5, -\frac{1}{3}w^{3} - \frac{2}{3}w^{2} + \frac{7}{3}w + 4]$ $\phantom{-}e$
5 $[5, 5, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{1}{3}w + 3]$ $-\frac{1}{2}e^{5} + 8e^{3} + 4e^{2} - \frac{13}{2}e + \frac{1}{2}$
9 $[9, 3, -w]$ $\phantom{-}4e^{5} + 3e^{4} - \frac{127}{2}e^{3} - \frac{161}{2}e^{2} + 16e + \frac{43}{2}$
9 $[9, 3, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{7}{3}w + 1]$ $\phantom{-}\frac{3}{2}e^{5} + \frac{1}{2}e^{4} - 24e^{3} - \frac{41}{2}e^{2} + 15e + 4$
16 $[16, 2, 2]$ $\phantom{-}\frac{3}{2}e^{5} + e^{4} - 24e^{3} - 28e^{2} + \frac{17}{2}e + \frac{13}{2}$
19 $[19, 19, \frac{2}{3}w^{3} - \frac{2}{3}w^{2} - \frac{11}{3}w]$ $-\frac{11}{2}e^{5} - \frac{9}{2}e^{4} + 87e^{3} + \frac{233}{2}e^{2} - 15e - 33$
19 $[19, 19, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{1}{3}w + 1]$ $-\frac{9}{2}e^{5} - \frac{7}{2}e^{4} + \frac{143}{2}e^{3} + 93e^{2} - 20e - \frac{61}{2}$
31 $[31, 31, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{11}{3}w - 2]$ $-e^{5} - e^{4} + 16e^{3} + 24e^{2} - 5e - 11$
31 $[31, 31, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{5}{3}w + 5]$ $-\frac{1}{2}e^{5} + e^{4} + \frac{17}{2}e^{3} - \frac{23}{2}e^{2} - \frac{41}{2}e + 4$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 6]$ $-\frac{21}{2}e^{5} - 7e^{4} + 167e^{3} + 197e^{2} - \frac{111}{2}e - \frac{107}{2}$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 3]$ $\phantom{-}\frac{11}{2}e^{5} + \frac{5}{2}e^{4} - \frac{175}{2}e^{3} - 85e^{2} + 41e + \frac{39}{2}$
61 $[61, 61, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} + \frac{2}{3}w + 4]$ $\phantom{-}1$
61 $[61, 61, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{14}{3}w - 2]$ $-\frac{1}{2}e^{5} - e^{4} + 8e^{3} + 20e^{2} + \frac{3}{2}e - \frac{33}{2}$
71 $[71, 71, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{1}{3}w - 7]$ $\phantom{-}2e^{5} + e^{4} - 31e^{3} - 33e^{2} + 3e + 4$
71 $[71, 71, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - \frac{7}{3}w]$ $-\frac{19}{2}e^{5} - 6e^{4} + \frac{303}{2}e^{3} + \frac{349}{2}e^{2} - \frac{121}{2}e - 57$
89 $[89, 89, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{10}{3}w - 3]$ $\phantom{-}e^{5} + \frac{1}{2}e^{4} - 15e^{3} - \frac{35}{2}e^{2} - \frac{11}{2}e + \frac{3}{2}$
89 $[89, 89, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w - 1]$ $\phantom{-}6e^{5} + 3e^{4} - \frac{191}{2}e^{3} - \frac{193}{2}e^{2} + 38e + \frac{35}{2}$
101 $[101, 101, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{7}{3}w - 3]$ $\phantom{-}13e^{5} + 10e^{4} - 207e^{3} - 265e^{2} + 61e + 82$
101 $[101, 101, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + \frac{11}{3}w - 4]$ $\phantom{-}\frac{11}{2}e^{5} + \frac{7}{2}e^{4} - 88e^{3} - \frac{201}{2}e^{2} + 40e + 31$
101 $[101, 101, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{8}{3}w + 3]$ $-3e^{5} - 3e^{4} + \frac{97}{2}e^{3} + \frac{143}{2}e^{2} - 19e - \frac{63}{2}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$61$ $[61, 61, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} + \frac{2}{3}w + 4]$ $-1$