Properties

 Label 4.4.5725.1-41.1-b Base field 4.4.5725.1 Weight $[2, 2, 2, 2]$ Level norm $41$ Level $[41, 41, \frac{2}{3}w^{3} + w^{2} - \frac{13}{3}w - \frac{10}{3}]$ Dimension $9$ CM no Base change no

Related objects

• L-function not available

Base field 4.4.5725.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 8x^{2} + 6x + 11$$; narrow class number $$1$$ and class number $$1$$.

Form

 Weight: $[2, 2, 2, 2]$ Level: $[41, 41, \frac{2}{3}w^{3} + w^{2} - \frac{13}{3}w - \frac{10}{3}]$ Dimension: $9$ CM: no Base change: no Newspace dimension: $15$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

 $$x^{9} - 2x^{8} - 43x^{7} + 94x^{6} + 446x^{5} - 1101x^{4} - 616x^{3} + 2034x^{2} + 270x - 914$$
Norm Prime Eigenvalue
9 $[9, 3, \frac{1}{3}w^{3} - \frac{8}{3}w - \frac{2}{3}]$ $\phantom{-}e$
9 $[9, 3, -w + 1]$ $...$
11 $[11, 11, w]$ $...$
11 $[11, 11, -\frac{1}{3}w^{3} + \frac{2}{3}w + \frac{5}{3}]$ $...$
11 $[11, 11, \frac{1}{3}w^{3} - \frac{8}{3}w + \frac{1}{3}]$ $...$
11 $[11, 11, -\frac{2}{3}w^{3} + \frac{13}{3}w + \frac{4}{3}]$ $...$
16 $[16, 2, 2]$ $...$
25 $[25, 5, \frac{2}{3}w^{3} - \frac{10}{3}w - \frac{1}{3}]$ $...$
29 $[29, 29, -w - 3]$ $...$
29 $[29, 29, -\frac{1}{3}w^{3} + \frac{8}{3}w - \frac{10}{3}]$ $...$
31 $[31, 31, w^{3} - 6w + 1]$ $...$
31 $[31, 31, w^{3} - 6w - 2]$ $...$
41 $[41, 41, \frac{2}{3}w^{3} + w^{2} - \frac{13}{3}w - \frac{10}{3}]$ $-1$
41 $[41, 41, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{5}{3}]$ $...$
59 $[59, 59, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{8}{3}]$ $...$
59 $[59, 59, w^{3} + w^{2} - 6w - 4]$ $...$
79 $[79, 79, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - \frac{19}{3}]$ $...$
79 $[79, 79, \frac{1}{3}w^{3} + w^{2} - \frac{2}{3}w - \frac{17}{3}]$ $...$
89 $[89, 89, \frac{4}{3}w^{3} - \frac{23}{3}w - \frac{5}{3}]$ $...$
89 $[89, 89, \frac{1}{3}w^{3} + 2w^{2} - \frac{5}{3}w - \frac{32}{3}]$ $...$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$41$ $[41, 41, \frac{2}{3}w^{3} + w^{2} - \frac{13}{3}w - \frac{10}{3}]$ $1$