Properties

 Base field 4.4.16997.1 Weight [2, 2, 2, 2] Level norm 25 Level $[25, 25, -w^{3} + 5w + 3]$ Label 4.4.16997.1-25.3-h Dimension 8 CM no Base change no

Related objects

• L-function not available

Base field 4.4.16997.1

Generator $$w$$, with minimal polynomial $$x^{4} - 6x^{2} - x + 5$$; narrow class number $$1$$ and class number $$1$$.

Form

 Weight [2, 2, 2, 2] Level $[25, 25, -w^{3} + 5w + 3]$ Label 4.4.16997.1-25.3-h Dimension 8 Is CM no Is base change no Parent newspace dimension 39

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{8} - 19x^{6} + 84x^{4} - 116x^{2} + 36$$
Norm Prime Eigenvalue
5 $[5, 5, w]$ $\phantom{-}\frac{3}{17}e^{6} - \frac{49}{17}e^{4} + \frac{127}{17}e^{2} - \frac{49}{17}$
5 $[5, 5, -w^{2} + w + 2]$ $\phantom{-}0$
7 $[7, 7, -w^{2} + 2]$ $\phantom{-}e$
13 $[13, 13, -w^{2} + 3]$ $-\frac{3}{34}e^{6} + \frac{49}{34}e^{4} - \frac{72}{17}e^{2} + \frac{67}{17}$
13 $[13, 13, w^{2} - w - 4]$ $\phantom{-}\frac{23}{102}e^{7} - \frac{202}{51}e^{5} + \frac{453}{34}e^{3} - \frac{389}{51}e$
16 $[16, 2, 2]$ $-\frac{4}{51}e^{7} + \frac{125}{102}e^{5} - \frac{77}{34}e^{3} - \frac{133}{51}e$
19 $[19, 19, -w^{2} + w + 1]$ $-\frac{5}{102}e^{7} + \frac{59}{102}e^{5} + \frac{28}{17}e^{3} - \frac{421}{51}e$
23 $[23, 23, -w^{3} + 4w + 2]$ $-\frac{4}{17}e^{6} + \frac{71}{17}e^{4} - \frac{243}{17}e^{2} + \frac{88}{17}$
25 $[25, 5, -w^{3} + w^{2} + 3w - 1]$ $-\frac{2}{17}e^{7} + \frac{71}{34}e^{5} - \frac{243}{34}e^{3} + \frac{44}{17}e$
29 $[29, 29, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}\frac{1}{17}e^{6} - \frac{22}{17}e^{4} + \frac{116}{17}e^{2} - \frac{124}{17}$
29 $[29, 29, -w + 3]$ $-\frac{3}{34}e^{6} + \frac{49}{34}e^{4} - \frac{55}{17}e^{2} - \frac{69}{17}$
31 $[31, 31, -w^{3} + w^{2} + 5w - 2]$ $\phantom{-}\frac{3}{34}e^{7} - \frac{49}{34}e^{5} + \frac{55}{17}e^{3} + \frac{35}{17}e$
37 $[37, 37, w^{3} - 4w - 1]$ $-\frac{8}{51}e^{7} + \frac{301}{102}e^{5} - \frac{443}{34}e^{3} + \frac{1009}{51}e$
37 $[37, 37, w^{3} - 3w + 1]$ $-\frac{7}{34}e^{6} + \frac{137}{34}e^{4} - \frac{321}{17}e^{2} + \frac{281}{17}$
53 $[53, 53, -w^{3} + 2w^{2} + 4w - 6]$ $-\frac{49}{102}e^{7} + \frac{437}{51}e^{5} - \frac{1039}{34}e^{3} + \frac{1168}{51}e$
59 $[59, 59, w^{2} + w - 4]$ $\phantom{-}\frac{2}{51}e^{7} - \frac{44}{51}e^{5} + \frac{83}{17}e^{3} - \frac{367}{51}e$
61 $[61, 61, -2w^{2} + w + 8]$ $-\frac{67}{102}e^{7} + \frac{1219}{102}e^{5} - \frac{774}{17}e^{3} + \frac{1978}{51}e$
73 $[73, 73, -w^{3} + 5w - 1]$ $\phantom{-}\frac{13}{17}e^{7} - \frac{453}{34}e^{5} + \frac{1503}{34}e^{3} - \frac{609}{17}e$
79 $[79, 79, 2w^{2} + w - 6]$ $-\frac{8}{17}e^{6} + \frac{142}{17}e^{4} - \frac{486}{17}e^{2} + \frac{244}{17}$
79 $[79, 79, 2w^{3} - w^{2} - 9w + 3]$ $-\frac{1}{34}e^{6} + \frac{5}{34}e^{4} + \frac{78}{17}e^{2} - \frac{278}{17}$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -w^{2} + w + 2]$ $-1$