# Properties

 Label 4.4.19429.1-17.1-c Base field 4.4.19429.1 Weight $[2, 2, 2, 2]$ Level norm $17$ Level $[17, 17, -w + 2]$ Dimension $22$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.19429.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 7x^{2} - x + 5$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[17, 17, -w + 2]$ Dimension: $22$ CM: no Base change: no Newspace dimension: $41$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{22} - x^{21} - 46x^{20} + 35x^{19} + 906x^{18} - 467x^{17} - 9976x^{16} + 2732x^{15} + 67157x^{14} - 3122x^{13} - 283673x^{12} - 44592x^{11} + 742374x^{10} + 245056x^{9} - 1145851x^{8} - 537750x^{7} + 943518x^{6} + 547736x^{5} - 340124x^{4} - 243704x^{3} + 25776x^{2} + 39200x + 6272$$
Norm Prime Eigenvalue
3 $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}e$
5 $[5, 5, w]$ $...$
7 $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ $...$
13 $[13, 13, -w^{2} + w + 4]$ $...$
13 $[13, 13, -w^{3} + 2w^{2} + 5w - 2]$ $...$
16 $[16, 2, 2]$ $...$
17 $[17, 17, -w + 2]$ $-1$
19 $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ $...$
27 $[27, 3, w^{3} - 3w^{2} - 4w + 7]$ $...$
31 $[31, 31, w^{3} - 3w^{2} - 3w + 7]$ $...$
31 $[31, 31, -w^{3} + w^{2} + 6w + 1]$ $...$
41 $[41, 41, w^{2} - w - 1]$ $...$
43 $[43, 43, 2w^{3} - 5w^{2} - 6w + 4]$ $...$
47 $[47, 47, -w^{3} + 2w^{2} + 5w - 1]$ $...$
53 $[53, 53, -w - 3]$ $...$
53 $[53, 53, -w^{3} + 3w^{2} + 3w - 6]$ $...$
59 $[59, 59, 2w^{2} - 3w - 6]$ $...$
59 $[59, 59, w^{3} - w^{2} - 7w - 3]$ $...$
79 $[79, 79, 2w^{3} - 4w^{2} - 8w + 3]$ $...$
79 $[79, 79, w^{2} - 2w - 1]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$17$ $[17, 17, -w + 2]$ $1$