# Properties

 Label 4.4.17609.1-11.1-b Base field 4.4.17609.1 Weight $[2, 2, 2, 2]$ Level norm $11$ Level $[11, 11, -w^{3} + 6w - 4]$ Dimension $13$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.17609.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 7x^{2} + 10x - 1$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[11, 11, -w^{3} + 6w - 4]$ Dimension: $13$ CM: no Base change: no Newspace dimension: $26$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{13} + 4x^{12} - 11x^{11} - 56x^{10} + 31x^{9} + 282x^{8} + 27x^{7} - 622x^{6} - 214x^{5} + 579x^{4} + 250x^{3} - 175x^{2} - 81x - 1$$
Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}e$
5 $[5, 5, w^{3} + w^{2} - 4w + 1]$ $...$
7 $[7, 7, -w^{3} + 6w - 2]$ $...$
8 $[8, 2, w^{3} - 7w + 3]$ $...$
11 $[11, 11, -w^{3} + 6w - 4]$ $\phantom{-}1$
17 $[17, 17, w^{3} + w^{2} - 6w - 1]$ $...$
17 $[17, 17, -w^{2} - w + 3]$ $...$
31 $[31, 31, 2w^{3} + w^{2} - 13w + 3]$ $...$
37 $[37, 37, -3w^{3} - w^{2} + 18w - 3]$ $...$
41 $[41, 41, w^{2} + 2w - 4]$ $...$
47 $[47, 47, 2w^{3} + 2w^{2} - 11w - 2]$ $...$
47 $[47, 47, -3w^{3} - w^{2} + 19w - 6]$ $...$
59 $[59, 59, -2w^{3} + 13w - 6]$ $...$
59 $[59, 59, -w^{3} - w^{2} + 5w + 2]$ $...$
59 $[59, 59, w^{2} + w - 1]$ $-\frac{48}{293}e^{12} - \frac{87}{293}e^{11} + \frac{700}{293}e^{10} + \frac{1230}{293}e^{9} - \frac{3556}{293}e^{8} - \frac{6563}{293}e^{7} + \frac{6816}{293}e^{6} + \frac{16704}{293}e^{5} - \frac{777}{293}e^{4} - \frac{19628}{293}e^{3} - \frac{9571}{293}e^{2} + \frac{7270}{293}e + \frac{3990}{293}$
59 $[59, 59, w^{2} + 2w - 6]$ $...$
61 $[61, 61, -w^{3} + w^{2} + 8w - 7]$ $...$
67 $[67, 67, w^{3} + 2w^{2} - 4w - 4]$ $...$
73 $[73, 73, -2w^{3} - w^{2} + 12w - 4]$ $...$
81 $[81, 3, -3]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$11$ $[11, 11, -w^{3} + 6w - 4]$ $-1$