Properties

 Base field 6.6.434581.1 Weight [2, 2, 2, 2, 2, 2] Level norm 71 Level $[71, 71, 2w^{4} - 4w^{3} - 6w^{2} + 7w + 2]$ Label 6.6.434581.1-71.2-f Dimension 3 CM no Base change no

Related objects

• L-function not available

Base field 6.6.434581.1

Generator $$w$$, with minimal polynomial $$x^{6} - 2x^{5} - 4x^{4} + 5x^{3} + 4x^{2} - 2x - 1$$; narrow class number $$1$$ and class number $$1$$.

Form

 Weight [2, 2, 2, 2, 2, 2] Level $[71, 71, 2w^{4} - 4w^{3} - 6w^{2} + 7w + 2]$ Label 6.6.434581.1-71.2-f Dimension 3 Is CM no Is base change no Parent newspace dimension 9

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{3} - 4x^{2} - 24x + 16$$
Norm Prime Eigenvalue
13 $[13, 13, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} + w + 4]$ $\phantom{-}e$
13 $[13, 13, -w^{2} + w + 2]$ $-e + 2$
27 $[27, 3, 2w^{5} - 4w^{4} - 7w^{3} + 9w^{2} + 4w - 2]$ $\phantom{-}2$
27 $[27, 3, -2w^{5} + 5w^{4} + 5w^{3} - 12w^{2} - w + 5]$ $\phantom{-}\frac{1}{4}e^{2} - \frac{3}{2}e - 5$
29 $[29, 29, w^{3} - 2w^{2} - 2w + 3]$ $\phantom{-}\frac{1}{4}e^{2} - e$
29 $[29, 29, 2w^{5} - 4w^{4} - 7w^{3} + 8w^{2} + 4w - 2]$ $-\frac{1}{4}e^{2} + 5$
43 $[43, 43, -w^{5} + 3w^{4} + w^{3} - 6w^{2} + 3w + 1]$ $-\frac{1}{2}e^{2} + e + 8$
43 $[43, 43, -w^{4} + w^{3} + 5w^{2} - 4]$ $-\frac{1}{2}e^{2} + \frac{7}{2}e + 11$
49 $[49, 7, w^{5} - 4w^{4} + 11w^{2} - 3w - 4]$ $-\frac{3}{2}e + 7$
64 $[64, 2, -2]$ $\phantom{-}\frac{1}{4}e^{2} + e - 13$
71 $[71, 71, 2w^{5} - 6w^{4} - 4w^{3} + 17w^{2} - w - 6]$ $\phantom{-}e - 7$
71 $[71, 71, 2w^{4} - 4w^{3} - 6w^{2} + 7w + 2]$ $-1$
71 $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w]$ $-e + 6$
71 $[71, 71, -2w^{5} + 5w^{4} + 6w^{3} - 14w^{2} - 3w + 5]$ $-\frac{1}{4}e^{2} + 2e + 6$
83 $[83, 83, -3w^{5} + 7w^{4} + 9w^{3} - 17w^{2} - 5w + 5]$ $\phantom{-}e - 6$
83 $[83, 83, 3w^{5} - 6w^{4} - 10w^{3} + 12w^{2} + 5w - 2]$ $\phantom{-}\frac{3}{4}e^{2} - 4e - 10$
83 $[83, 83, -2w^{5} + 5w^{4} + 5w^{3} - 11w^{2} - 3w + 3]$ $-\frac{3}{4}e^{2} + 4e + 11$
83 $[83, 83, 3w^{5} - 7w^{4} - 8w^{3} + 15w^{2} + 2w - 4]$ $-\frac{1}{2}e + 1$
97 $[97, 97, -3w^{5} + 6w^{4} + 10w^{3} - 12w^{2} - 5w + 3]$ $\phantom{-}\frac{1}{4}e^{2} - \frac{1}{2}e - 1$
97 $[97, 97, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w - 3]$ $\phantom{-}\frac{1}{2}e^{2} - e - 2$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
71 $[71, 71, 2w^{4} - 4w^{3} - 6w^{2} + 7w + 2]$ $1$