# Properties

 Base field 4.4.17725.1 Weight [2, 2, 2, 2] Level norm 16 Level $[16, 2, 2]$ Label 4.4.17725.1-16.1-f Dimension 6 CM no Base change no

# Related objects

• L-function not available

# Learn more about

## 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 $[16, 2, 2]$ Label 4.4.17725.1-16.1-f Dimension 6 Is CM no Is base change no Parent newspace dimension 30

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{6}$$ $$\mathstrut +\mathstrut 6x^{5}$$ $$\mathstrut -\mathstrut 15x^{4}$$ $$\mathstrut -\mathstrut 100x^{3}$$ $$\mathstrut +\mathstrut 128x^{2}$$ $$\mathstrut +\mathstrut 472x$$ $$\mathstrut -\mathstrut 667$$
Norm Prime Eigenvalue
9 $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ $\phantom{-}e$
9 $[9, 3, -w^{3} + 8w + 8]$ $-e - 2$
16 $[16, 2, 2]$ $\phantom{-}1$
19 $[19, 19, w + 1]$ $\phantom{-}\frac{1}{7}e^{5} + \frac{5}{7}e^{4} - \frac{6}{7}e^{3} - \frac{38}{7}e^{2} + \frac{5}{7}e + \frac{40}{7}$
19 $[19, 19, -w^{2} + 6]$ $-\frac{1}{7}e^{5} - \frac{5}{7}e^{4} + \frac{13}{7}e^{3} + \frac{59}{7}e^{2} - \frac{61}{7}e - \frac{124}{7}$
19 $[19, 19, -w^{2} + 2w + 5]$ $\phantom{-}\frac{1}{7}e^{5} + \frac{5}{7}e^{4} - \frac{13}{7}e^{3} - \frac{59}{7}e^{2} + \frac{61}{7}e + \frac{82}{7}$
19 $[19, 19, -w + 2]$ $-\frac{1}{7}e^{5} - \frac{5}{7}e^{4} + \frac{6}{7}e^{3} + \frac{38}{7}e^{2} - \frac{5}{7}e - \frac{26}{7}$
25 $[25, 5, 2w^{2} - 2w - 13]$ $-e^{2} - 2e + 6$
29 $[29, 29, -w^{2} + 9]$ $-\frac{1}{7}e^{5} - \frac{12}{7}e^{4} - \frac{22}{7}e^{3} + \frac{143}{7}e^{2} + \frac{254}{7}e - \frac{642}{7}$
29 $[29, 29, -w^{2} + 2w + 6]$ $\phantom{-}\frac{1}{7}e^{5} + \frac{12}{7}e^{4} + \frac{15}{7}e^{3} - \frac{157}{7}e^{2} - \frac{198}{7}e + \frac{635}{7}$
29 $[29, 29, w^{2} - 7]$ $-\frac{1}{7}e^{5} + \frac{2}{7}e^{4} + \frac{41}{7}e^{3} - \frac{39}{7}e^{2} - \frac{306}{7}e + \frac{443}{7}$
29 $[29, 29, -w^{2} + 2w + 8]$ $\phantom{-}\frac{1}{7}e^{5} - \frac{2}{7}e^{4} - \frac{34}{7}e^{3} + \frac{67}{7}e^{2} + \frac{278}{7}e - \frac{562}{7}$
31 $[31, 31, -2w^{2} + w + 12]$ $-\frac{2}{7}e^{5} - \frac{10}{7}e^{4} + \frac{19}{7}e^{3} + \frac{104}{7}e^{2} - \frac{59}{7}e - \frac{206}{7}$
31 $[31, 31, 2w^{2} - 3w - 11]$ $\phantom{-}\frac{2}{7}e^{5} + \frac{10}{7}e^{4} - \frac{19}{7}e^{3} - \frac{90}{7}e^{2} + \frac{87}{7}e + \frac{80}{7}$
41 $[41, 41, -w]$ $\phantom{-}\frac{1}{7}e^{5} - \frac{2}{7}e^{4} - \frac{34}{7}e^{3} + \frac{60}{7}e^{2} + \frac{257}{7}e - \frac{492}{7}$
41 $[41, 41, -w + 1]$ $-\frac{1}{7}e^{5} - \frac{12}{7}e^{4} - \frac{22}{7}e^{3} + \frac{136}{7}e^{2} + \frac{247}{7}e - \frac{558}{7}$
49 $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ $-\frac{1}{7}e^{5} + \frac{2}{7}e^{4} + \frac{34}{7}e^{3} - \frac{60}{7}e^{2} - \frac{264}{7}e + \frac{478}{7}$
49 $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ $\phantom{-}\frac{1}{7}e^{5} + \frac{12}{7}e^{4} + \frac{22}{7}e^{3} - \frac{136}{7}e^{2} - \frac{240}{7}e + \frac{558}{7}$
61 $[61, 61, 2w^{2} - 3w - 14]$ $\phantom{-}\frac{1}{7}e^{5} + \frac{12}{7}e^{4} + \frac{22}{7}e^{3} - \frac{157}{7}e^{2} - \frac{275}{7}e + \frac{789}{7}$
61 $[61, 61, 2w^{2} - w - 15]$ $-\frac{1}{7}e^{5} + \frac{2}{7}e^{4} + \frac{34}{7}e^{3} - \frac{81}{7}e^{2} - \frac{313}{7}e + \frac{695}{7}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
16 $[16, 2, 2]$ $-1$