Properties

 Base field $$\Q(\sqrt{5}, \sqrt{7})$$ Weight [2, 2, 2, 2] Level norm 16 Level $[16, 2, 2]$ Label 4.4.19600.1-16.1-i Dimension 4 CM no Base change no

Related objects

• L-function not available

Base field $$\Q(\sqrt{5}, \sqrt{7})$$

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 15x^{2} + 16x + 29$$; narrow class number $$2$$ and class number $$1$$.

Form

 Weight [2, 2, 2, 2] Level $[16, 2, 2]$ Label 4.4.19600.1-16.1-i Dimension 4 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:
$$x^{4}$$ $$\mathstrut +\mathstrut 8x^{3}$$ $$\mathstrut +\mathstrut 6x^{2}$$ $$\mathstrut -\mathstrut 40x$$ $$\mathstrut -\mathstrut 20$$
Norm Prime Eigenvalue
4 $[4, 2, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w + \frac{1}{23}]$ $\phantom{-}0$
9 $[9, 3, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w + \frac{24}{23}]$ $-\frac{1}{6}e^{3} - e^{2} + \frac{5}{3}$
9 $[9, 3, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w - \frac{68}{23}]$ $\phantom{-}\frac{1}{6}e^{3} + e^{2} - \frac{11}{3}$
19 $[19, 19, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w + \frac{24}{23}]$ $\phantom{-}e$
19 $[19, 19, -\frac{6}{23}w^{3} + \frac{9}{23}w^{2} + \frac{83}{23}w - \frac{20}{23}]$ $\phantom{-}e + 4$
19 $[19, 19, \frac{6}{23}w^{3} - \frac{9}{23}w^{2} - \frac{83}{23}w + \frac{66}{23}]$ $-\frac{1}{6}e^{3} - e^{2} + e + \frac{20}{3}$
19 $[19, 19, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w - \frac{22}{23}]$ $-\frac{1}{6}e^{3} - e^{2} + e + \frac{8}{3}$
25 $[25, 5, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{40}{23}w - \frac{21}{23}]$ $-4$
29 $[29, 29, w]$ $-\frac{1}{3}e^{3} - \frac{7}{3}e^{2} + \frac{2}{3}e + 9$
29 $[29, 29, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{63}{23}w - \frac{21}{23}]$ $\phantom{-}\frac{1}{3}e^{2} - \frac{2}{3}e - \frac{23}{3}$
29 $[29, 29, \frac{4}{23}w^{3} - \frac{6}{23}w^{2} - \frac{63}{23}w + \frac{44}{23}]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{5}{3}e^{2} - \frac{10}{3}e - \frac{29}{3}$
29 $[29, 29, -w + 1]$ $\phantom{-}\frac{1}{3}e^{2} + \frac{10}{3}e + \frac{1}{3}$
31 $[31, 31, w + 2]$ $\phantom{-}\frac{1}{6}e^{3} + \frac{2}{3}e^{2} - \frac{7}{3}e - 8$
31 $[31, 31, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{63}{23}w + \frac{25}{23}]$ $-\frac{1}{3}e^{2} - \frac{7}{3}e + \frac{14}{3}$
31 $[31, 31, \frac{4}{23}w^{3} - \frac{6}{23}w^{2} - \frac{63}{23}w + \frac{90}{23}]$ $\phantom{-}\frac{1}{6}e^{3} + \frac{4}{3}e^{2} + \frac{1}{3}e - \frac{4}{3}$
31 $[31, 31, -w + 3]$ $\phantom{-}\frac{1}{3}e^{2} + \frac{1}{3}e - \frac{26}{3}$
49 $[49, 7, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w - \frac{22}{23}]$ $\phantom{-}6$
59 $[59, 59, -\frac{20}{23}w^{3} + \frac{30}{23}w^{2} + \frac{269}{23}w - \frac{128}{23}]$ $-\frac{2}{3}e^{2} - \frac{14}{3}e + \frac{4}{3}$
59 $[59, 59, -\frac{8}{23}w^{3} + \frac{12}{23}w^{2} + \frac{103}{23}w - \frac{88}{23}]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{4}{3}e^{2} - \frac{14}{3}e - 8$
59 $[59, 59, -\frac{8}{23}w^{3} + \frac{12}{23}w^{2} + \frac{103}{23}w - \frac{19}{23}]$ $\phantom{-}\frac{2}{3}e^{2} + \frac{2}{3}e - \frac{28}{3}$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
4 $[4,2,-\frac{2}{23}w^{3}+\frac{3}{23}w^{2}-\frac{3}{23}w+\frac{1}{23}]$ $-1$