Properties

 Base field 4.4.19225.1 Weight [2, 2, 2, 2] Level norm 25 Level $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ Label 4.4.19225.1-25.1-e Dimension 6 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 $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ Label 4.4.19225.1-25.1-e Dimension 6 Is CM no Is base change no Parent newspace dimension 63

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{6} - 4x^{5} - 11x^{4} + 42x^{3} + 39x^{2} - 99x - 27$$
Norm Prime Eigenvalue
4 $[4, 2, w + 2]$ $\phantom{-}e$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{2}{3}e^{2} - 3e + 3$
9 $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{5}{2}w + 17]$ $-\frac{1}{3}e^{4} + e^{3} + \frac{4}{3}e^{2} - 4e + 4$
9 $[9, 3, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 28]$ $\phantom{-}e^{2} - e - 5$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 11]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - 4e - 2$
11 $[11, 11, -w - 3]$ $-\frac{1}{3}e^{4} + e^{3} + \frac{4}{3}e^{2} - 3e + 4$
25 $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ $-1$
29 $[29, 29, w + 1]$ $\phantom{-}\frac{1}{3}e^{4} - \frac{13}{3}e^{2} - 2e + 9$
29 $[29, 29, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 9]$ $\phantom{-}\frac{1}{3}e^{4} - \frac{1}{3}e^{3} - \frac{11}{3}e^{2} + 2e + 6$
31 $[31, 31, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 16]$ $\phantom{-}\frac{2}{3}e^{3} - \frac{1}{3}e^{2} - 6e - 1$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 5]$ $\phantom{-}e + 1$
31 $[31, 31, -w + 3]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{2}{3}e^{2} - 3e + 4$
31 $[31, 31, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 29]$ $-\frac{1}{3}e^{4} + \frac{4}{3}e^{3} + \frac{2}{3}e^{2} - 5e + 5$
59 $[59, 59, 2w^{2} - w - 13]$ $\phantom{-}2e^{2} - 3e - 8$
59 $[59, 59, \frac{9}{2}w^{3} - \frac{31}{2}w^{2} - \frac{61}{2}w + 85]$ $-\frac{2}{3}e^{4} + \frac{5}{3}e^{3} + \frac{10}{3}e^{2} - 5e + 7$
61 $[61, 61, 2w^{3} - 6w^{2} - 15w + 31]$ $\phantom{-}\frac{1}{3}e^{5} - \frac{1}{3}e^{4} - \frac{14}{3}e^{3} + e^{2} + 16e + 1$
61 $[61, 61, -\frac{3}{2}w^{3} + \frac{11}{2}w^{2} + \frac{21}{2}w - 34]$ $-\frac{1}{3}e^{5} + 2e^{4} - \frac{40}{3}e^{2} + 7e + 10$
71 $[71, 71, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 32]$ $\phantom{-}\frac{2}{3}e^{4} - 3e^{3} - \frac{5}{3}e^{2} + 15e - 6$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 13]$ $\phantom{-}\frac{1}{3}e^{4} - 2e^{3} - \frac{4}{3}e^{2} + 12e + 3$
79 $[79, 79, -3w^{3} + 10w^{2} + 19w - 51]$ $-e^{4} + 2e^{3} + 8e^{2} - 7e - 10$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
25 $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ $1$