# Properties

 Base field 4.4.19225.1 Weight [2, 2, 2, 2] Level norm 16 Level $[16, 4, w^{3} - 3w^{2} - 8w + 16]$ Label 4.4.19225.1-16.2-c Dimension 5 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.19225.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 15x^{2} + 2x + 44$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[16, 4, w^{3} - 3w^{2} - 8w + 16]$ Label 4.4.19225.1-16.2-c Dimension 5 Is CM no Is base change no Parent newspace dimension 26

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{5} - x^{4} - 13x^{3} + 25x^{2} - 2x - 12$$
Norm Prime Eigenvalue
4 $[4, 2, w + 2]$ $\phantom{-}0$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ $\phantom{-}e$
9 $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{5}{2}w + 17]$ $\phantom{-}e^{4} + e^{3} - 12e^{2} + 2e + 11$
9 $[9, 3, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 28]$ $-\frac{3}{2}e^{4} - \frac{1}{2}e^{3} + \frac{37}{2}e^{2} - \frac{25}{2}e - 10$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 11]$ $-e^{4} + 13e^{2} - 12e - 8$
11 $[11, 11, -w - 3]$ $\phantom{-}3e^{4} + e^{3} - 38e^{2} + 25e + 27$
25 $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ $\phantom{-}4e^{4} + e^{3} - 51e^{2} + 35e + 35$
29 $[29, 29, w + 1]$ $-\frac{3}{2}e^{4} - \frac{1}{2}e^{3} + \frac{39}{2}e^{2} - \frac{23}{2}e - 16$
29 $[29, 29, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 9]$ $\phantom{-}4e^{4} + e^{3} - 51e^{2} + 35e + 36$
31 $[31, 31, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 16]$ $\phantom{-}\frac{3}{2}e^{4} + \frac{1}{2}e^{3} - \frac{37}{2}e^{2} + \frac{27}{2}e + 16$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 5]$ $-5e^{4} - 2e^{3} + 62e^{2} - 38e - 37$
31 $[31, 31, -w + 3]$ $-2e + 2$
31 $[31, 31, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 29]$ $-\frac{13}{2}e^{4} - \frac{5}{2}e^{3} + \frac{161}{2}e^{2} - \frac{99}{2}e - 55$
59 $[59, 59, 2w^{2} - w - 13]$ $-10e^{4} - 4e^{3} + 125e^{2} - 76e - 89$
59 $[59, 59, \frac{9}{2}w^{3} - \frac{31}{2}w^{2} - \frac{61}{2}w + 85]$ $-e^{4} + 13e^{2} - 10e$
61 $[61, 61, 2w^{3} - 6w^{2} - 15w + 31]$ $-3e^{4} - 2e^{3} + 37e^{2} - 14e - 29$
61 $[61, 61, -\frac{3}{2}w^{3} + \frac{11}{2}w^{2} + \frac{21}{2}w - 34]$ $\phantom{-}\frac{7}{2}e^{4} + \frac{3}{2}e^{3} - \frac{87}{2}e^{2} + \frac{49}{2}e + 36$
71 $[71, 71, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 32]$ $\phantom{-}\frac{21}{2}e^{4} + \frac{9}{2}e^{3} - \frac{259}{2}e^{2} + \frac{155}{2}e + 88$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 13]$ $\phantom{-}\frac{7}{2}e^{4} + \frac{1}{2}e^{3} - \frac{91}{2}e^{2} + \frac{63}{2}e + 41$
79 $[79, 79, -3w^{3} + 10w^{2} + 19w - 51]$ $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + \frac{15}{2}e^{2} - \frac{21}{2}e - 2$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w + 2]$ $1$