# Properties

 Label 4.4.18097.1-13.1-a Base field 4.4.18097.1 Weight $[2, 2, 2, 2]$ Level norm $13$ Level $[13, 13, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - 1]$ Dimension $10$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.18097.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 7x^{2} + 6x + 4$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[13, 13, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - 1]$ Dimension: $10$ CM: no Base change: no Newspace dimension: $28$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{10} - 18x^{8} + 118x^{6} - 333x^{4} + 345x^{2} - 16$$
Norm Prime Eigenvalue
3 $[3, 3, -w + 1]$ $\phantom{-}e$
4 $[4, 2, w]$ $\phantom{-}\frac{1}{4}e^{9} - \frac{7}{2}e^{7} + \frac{33}{2}e^{5} - \frac{117}{4}e^{3} + \frac{57}{4}e$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - 3]$ $-\frac{3}{4}e^{9} + \frac{19}{2}e^{7} - \frac{79}{2}e^{5} + \frac{235}{4}e^{3} - \frac{71}{4}e$
7 $[7, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{5}{2}w - 2]$ $-2e^{8} + 25e^{6} - 100e^{4} + 130e^{2} - 8$
13 $[13, 13, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - 1]$ $\phantom{-}1$
17 $[17, 17, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w]$ $\phantom{-}\frac{1}{2}e^{9} - 6e^{7} + 23e^{5} - \frac{59}{2}e^{3} + \frac{5}{2}e$
27 $[27, 3, -w^{3} + 7w + 1]$ $-2e^{9} + 25e^{7} - 99e^{5} + 122e^{3} + 7e$
31 $[31, 31, w + 3]$ $-e^{6} + 9e^{4} - 19e^{2}$
31 $[31, 31, -w^{2} + 5]$ $-e^{9} + 11e^{7} - 36e^{5} + 33e^{3} + 4e$
37 $[37, 37, w^{2} - 3]$ $\phantom{-}\frac{5}{2}e^{9} - 30e^{7} + 112e^{5} - \frac{251}{2}e^{3} - \frac{33}{2}e$
41 $[41, 41, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{3}{2}w - 2]$ $-\frac{3}{2}e^{9} + 18e^{7} - 67e^{5} + \frac{149}{2}e^{3} + \frac{17}{2}e$
47 $[47, 47, w^{3} - 5w - 3]$ $\phantom{-}2e^{9} - 24e^{7} + 93e^{5} - 129e^{3} + 40e$
53 $[53, 53, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w]$ $\phantom{-}\frac{1}{2}e^{9} - 6e^{7} + 21e^{5} - \frac{25}{2}e^{3} - \frac{57}{2}e$
61 $[61, 61, w^{3} - w^{2} - 5w + 3]$ $\phantom{-}e^{6} - 8e^{4} + 13e^{2} - 2$
83 $[83, 83, w^{3} + w^{2} - 6w - 7]$ $\phantom{-}2e^{9} - 26e^{7} + 111e^{5} - 169e^{3} + 53e$
83 $[83, 83, -w^{3} + 5w + 1]$ $\phantom{-}2e^{8} - 24e^{6} + 91e^{4} - 112e^{2} + 4$
83 $[83, 83, 2w - 1]$ $\phantom{-}2e^{9} - 26e^{7} + 114e^{5} - 191e^{3} + 85e$
83 $[83, 83, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 2]$ $\phantom{-}9e^{8} - 109e^{6} + 416e^{4} - 506e^{2} + 20$
89 $[89, 89, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w - 2]$ $-5e^{8} + 60e^{6} - 225e^{4} + 263e^{2} - 6$
89 $[89, 89, w^{3} - 5w + 5]$ $\phantom{-}e^{8} - 15e^{6} + 72e^{4} - 107e^{2} - 6$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - 1]$ $-1$