# Properties

 Label 4.4.5725.1-59.1-c Base field 4.4.5725.1 Weight $[2, 2, 2, 2]$ Level norm $59$ Level $[59, 59, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{8}{3}]$ Dimension $13$ 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: $[59, 59, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{8}{3}]$ Dimension: $13$ CM: no Base change: no Newspace dimension: $18$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{13} - 13x^{12} + 12x^{11} + 474x^{10} - 1879x^{9} - 1896x^{8} + 18824x^{7} - 13900x^{6} - 42512x^{5} + 37936x^{4} + 44992x^{3} - 23680x^{2} - 23040x - 2304$$
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 $[41, 41, \frac{2}{3}w^{3} + w^{2} - \frac{13}{3}w - \frac{10}{3}]$ $...$
41 $[41, 41, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{5}{3}]$ $...$
59 $[59, 59, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{8}{3}]$ $-1$
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
$59$ $[59, 59, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{8}{3}]$ $1$