# Properties

 Base field 4.4.17725.1 Weight [2, 2, 2, 2] Level norm 1 Level $[1, 1, 1]$ Label 4.4.17725.1-1.1-a Dimension 6 CM no Base change yes

# Related objects

• L-function not available

## Base field 4.4.17725.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 12x^{2} + 13x + 41$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[1, 1, 1]$ Label 4.4.17725.1-1.1-a Dimension 6 Is CM no Is base change yes Parent newspace dimension 6

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{6} + 2x^{5} - 35x^{4} - 46x^{3} + 310x^{2} + 116x - 375$$
Norm Prime Eigenvalue
9 $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ $\phantom{-}e$
9 $[9, 3, -w^{3} + 8w + 8]$ $\phantom{-}e$
16 $[16, 2, 2]$ $-\frac{1}{42}e^{5} + \frac{7}{12}e^{3} - \frac{9}{28}e^{2} - \frac{73}{42}e + \frac{167}{28}$
19 $[19, 19, w + 1]$ $\phantom{-}\frac{1}{84}e^{5} + \frac{1}{12}e^{4} - \frac{1}{4}e^{3} - \frac{43}{21}e^{2} + \frac{19}{42}e + \frac{165}{28}$
19 $[19, 19, -w^{2} + 6]$ $-\frac{1}{12}e^{4} + \frac{1}{12}e^{3} + \frac{11}{6}e^{2} - \frac{31}{12}e - \frac{5}{2}$
19 $[19, 19, -w^{2} + 2w + 5]$ $-\frac{1}{12}e^{4} + \frac{1}{12}e^{3} + \frac{11}{6}e^{2} - \frac{31}{12}e - \frac{5}{2}$
19 $[19, 19, -w + 2]$ $\phantom{-}\frac{1}{84}e^{5} + \frac{1}{12}e^{4} - \frac{1}{4}e^{3} - \frac{43}{21}e^{2} + \frac{19}{42}e + \frac{165}{28}$
25 $[25, 5, 2w^{2} - 2w - 13]$ $\phantom{-}\frac{1}{84}e^{5} + \frac{1}{12}e^{4} - \frac{1}{4}e^{3} - \frac{43}{21}e^{2} + \frac{19}{42}e + \frac{333}{28}$
29 $[29, 29, -w^{2} + 9]$ $\phantom{-}\frac{1}{42}e^{5} - \frac{5}{6}e^{3} + \frac{1}{14}e^{2} + \frac{241}{42}e - \frac{5}{7}$
29 $[29, 29, -w^{2} + 2w + 6]$ $-\frac{1}{84}e^{5} + \frac{5}{12}e^{3} + \frac{13}{28}e^{2} - \frac{241}{84}e - \frac{65}{14}$
29 $[29, 29, w^{2} - 7]$ $-\frac{1}{84}e^{5} + \frac{5}{12}e^{3} + \frac{13}{28}e^{2} - \frac{241}{84}e - \frac{65}{14}$
29 $[29, 29, -w^{2} + 2w + 8]$ $\phantom{-}\frac{1}{42}e^{5} - \frac{5}{6}e^{3} + \frac{1}{14}e^{2} + \frac{241}{42}e - \frac{5}{7}$
31 $[31, 31, -2w^{2} + w + 12]$ $-\frac{1}{42}e^{5} - \frac{1}{12}e^{4} + \frac{2}{3}e^{3} + \frac{127}{84}e^{2} - \frac{121}{28}e - \frac{43}{28}$
31 $[31, 31, 2w^{2} - 3w - 11]$ $-\frac{1}{42}e^{5} - \frac{1}{12}e^{4} + \frac{2}{3}e^{3} + \frac{127}{84}e^{2} - \frac{121}{28}e - \frac{43}{28}$
41 $[41, 41, -w]$ $-\frac{1}{4}e^{3} - \frac{1}{4}e^{2} + 4e + \frac{1}{4}$
41 $[41, 41, -w + 1]$ $-\frac{1}{4}e^{3} - \frac{1}{4}e^{2} + 4e + \frac{1}{4}$
49 $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ $-\frac{1}{84}e^{5} - \frac{1}{12}e^{4} + \frac{1}{2}e^{3} + \frac{193}{84}e^{2} - \frac{229}{42}e - \frac{50}{7}$
49 $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ $-\frac{1}{84}e^{5} - \frac{1}{12}e^{4} + \frac{1}{2}e^{3} + \frac{193}{84}e^{2} - \frac{229}{42}e - \frac{50}{7}$
61 $[61, 61, 2w^{2} - 3w - 14]$ $-\frac{1}{42}e^{5} + \frac{1}{12}e^{4} + \frac{3}{4}e^{3} - \frac{40}{21}e^{2} - \frac{349}{84}e + \frac{31}{14}$
61 $[61, 61, 2w^{2} - w - 15]$ $-\frac{1}{42}e^{5} + \frac{1}{12}e^{4} + \frac{3}{4}e^{3} - \frac{40}{21}e^{2} - \frac{349}{84}e + \frac{31}{14}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is $$(1)$$.