# Properties

 Label 4.4.15188.1-13.1-b Base field 4.4.15188.1 Weight $[2, 2, 2, 2]$ Level norm $13$ Level $[13, 13, -w^{3} + w^{2} + 6w - 3]$ Dimension $18$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.15188.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 7x^{2} + x + 2$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[13, 13, -w^{3} + w^{2} + 6w - 3]$ Dimension: $18$ CM: no Base change: no Newspace dimension: $36$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{18} + 4x^{17} - 19x^{16} - 90x^{15} + 124x^{14} + 814x^{13} - 222x^{12} - 3802x^{11} - 1023x^{10} + 9774x^{9} + 5785x^{8} - 13540x^{7} - 11139x^{6} + 8912x^{5} + 9483x^{4} - 1598x^{3} - 2988x^{2} - 436x + 40$$
Norm Prime Eigenvalue
2 $[2, 2, w]$ $...$
2 $[2, 2, -\frac{1}{2}w^{3} + w^{2} + \frac{3}{2}w]$ $\phantom{-}e$
11 $[11, 11, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 4]$ $...$
11 $[11, 11, -w^{3} + w^{2} + 6w + 1]$ $...$
13 $[13, 13, -w^{3} + w^{2} + 6w - 3]$ $\phantom{-}1$
19 $[19, 19, -\frac{1}{2}w^{3} + w^{2} + \frac{5}{2}w]$ $...$
23 $[23, 23, -\frac{1}{2}w^{3} + 2w^{2} - \frac{1}{2}w - 2]$ $...$
31 $[31, 31, -w^{3} + w^{2} + 6w - 1]$ $...$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{7}{2}w]$ $...$
43 $[43, 43, \frac{1}{2}w^{3} - w^{2} - \frac{9}{2}w + 2]$ $...$
67 $[67, 67, w^{2} - w - 5]$ $...$
67 $[67, 67, -\frac{1}{2}w^{3} + \frac{11}{2}w + 2]$ $...$
73 $[73, 73, w^{2} + w + 1]$ $...$
79 $[79, 79, \frac{1}{2}w^{3} + w^{2} - \frac{5}{2}w - 2]$ $...$
81 $[81, 3, -3]$ $...$
83 $[83, 83, 2w^{3} - 2w^{2} - 12w + 5]$ $...$
83 $[83, 83, -\frac{1}{2}w^{3} - w^{2} + \frac{1}{2}w + 2]$ $...$
89 $[89, 89, -\frac{3}{2}w^{3} + 2w^{2} + \frac{17}{2}w - 2]$ $...$
89 $[89, 89, \frac{3}{2}w^{3} - 2w^{2} - \frac{21}{2}w + 2]$ $...$
97 $[97, 97, \frac{1}{2}w^{3} - w^{2} - \frac{1}{2}w - 2]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, -w^{3} + w^{2} + 6w - 3]$ $-1$