# Properties

 Label 4.4.19525.1-16.1-e Base field 4.4.19525.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 2, 2]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.19525.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 14x^{2} + 15x + 45$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[16, 2, 2]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $36$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} + 2x^{3} - 11x^{2} - 2x + 11$$
Norm Prime Eigenvalue
5 $[5, 5, \frac{2}{3}w^{2} + \frac{1}{3}w - 5]$ $\phantom{-}e$
5 $[5, 5, \frac{2}{3}w^{2} - \frac{5}{3}w - 4]$ $\phantom{-}\frac{4}{11}e^{3} + \frac{10}{11}e^{2} - \frac{39}{11}e - 2$
9 $[9, 3, -w + 3]$ $-\frac{1}{11}e^{3} + \frac{3}{11}e^{2} + \frac{18}{11}e - 4$
9 $[9, 3, w + 2]$ $-\frac{3}{11}e^{3} - \frac{13}{11}e^{2} + \frac{10}{11}e + 2$
11 $[11, 11, \frac{2}{3}w^{2} + \frac{1}{3}w - 4]$ $\phantom{-}0$
16 $[16, 2, 2]$ $\phantom{-}1$
19 $[19, 19, \frac{1}{3}w^{3} - \frac{10}{3}w - 3]$ $\phantom{-}\frac{1}{11}e^{3} - \frac{3}{11}e^{2} - \frac{29}{11}e + 4$
19 $[19, 19, \frac{1}{3}w^{3} - w^{2} - \frac{7}{3}w + 6]$ $-\frac{1}{11}e^{3} + \frac{3}{11}e^{2} + \frac{29}{11}e$
29 $[29, 29, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 2]$ $-\frac{5}{11}e^{3} - \frac{7}{11}e^{2} + \frac{46}{11}e + 1$
29 $[29, 29, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $-\frac{7}{11}e^{3} - \frac{23}{11}e^{2} + \frac{38}{11}e + 7$
31 $[31, 31, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w + 1]$ $-\frac{1}{11}e^{3} + \frac{3}{11}e^{2} + \frac{7}{11}e - 6$
31 $[31, 31, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 4]$ $-\frac{7}{11}e^{3} - \frac{23}{11}e^{2} + \frac{49}{11}e + 2$
49 $[49, 7, \frac{1}{3}w^{3} - \frac{10}{3}w - 1]$ $-\frac{2}{11}e^{3} - \frac{16}{11}e^{2} + \frac{3}{11}e + 11$
49 $[49, 7, -\frac{1}{3}w^{3} + w^{2} + \frac{7}{3}w - 4]$ $\phantom{-}\frac{6}{11}e^{3} + \frac{26}{11}e^{2} - \frac{31}{11}e - 3$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{5}{3}w - 11]$ $\phantom{-}\frac{10}{11}e^{3} + \frac{36}{11}e^{2} - \frac{48}{11}e - 10$
59 $[59, 59, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 5w - 13]$ $\phantom{-}\frac{6}{11}e^{3} + \frac{4}{11}e^{2} - \frac{64}{11}e + 2$
61 $[61, 61, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{2}{3}w - 9]$ $\phantom{-}\frac{13}{11}e^{3} + \frac{38}{11}e^{2} - \frac{69}{11}e - 6$
61 $[61, 61, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 4w + 2]$ $-\frac{8}{11}e^{3} - \frac{20}{11}e^{2} + \frac{78}{11}e + 6$
61 $[61, 61, \frac{2}{3}w^{2} - \frac{5}{3}w - 1]$ $-2e + 2$
61 $[61, 61, -\frac{1}{3}w^{2} + \frac{4}{3}w + 6]$ $\phantom{-}\frac{15}{11}e^{3} + \frac{32}{11}e^{2} - \frac{127}{11}e - 2$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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