# Properties

 Base field $$\Q(\sqrt{113})$$ Weight [2, 2] Level norm 7 Level $[7,7,-6w - 29]$ Label 2.2.113.1-7.2-b Dimension 6 CM no Base change no

# Related objects

• L-function not available

## Base field $$\Q(\sqrt{113})$$

Generator $$w$$, with minimal polynomial $$x^{2} - x - 28$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2] Level $[7,7,-6w - 29]$ Label 2.2.113.1-7.2-b Dimension 6 Is CM no Is base change no Parent newspace dimension 17

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{6}$$ $$\mathstrut -\mathstrut x^{5}$$ $$\mathstrut -\mathstrut 9x^{4}$$ $$\mathstrut +\mathstrut 9x^{3}$$ $$\mathstrut +\mathstrut 14x^{2}$$ $$\mathstrut -\mathstrut 9x$$ $$\mathstrut -\mathstrut 1$$
Norm Prime Eigenvalue
2 $[2, 2, -w + 6]$ $\phantom{-}\frac{1}{7}e^{5} + \frac{2}{7}e^{4} - \frac{10}{7}e^{3} - 2e^{2} + 3e + \frac{12}{7}$
2 $[2, 2, w + 5]$ $\phantom{-}e$
7 $[7, 7, 6w - 35]$ $-\frac{2}{7}e^{5} + \frac{3}{7}e^{4} + \frac{20}{7}e^{3} - 3e^{2} - 6e - \frac{3}{7}$
7 $[7, 7, -6w - 29]$ $\phantom{-}1$
9 $[9, 3, 3]$ $-\frac{3}{7}e^{5} + \frac{1}{7}e^{4} + \frac{23}{7}e^{3} - 2e^{2} - 4e + \frac{13}{7}$
11 $[11, 11, 4w + 19]$ $-\frac{4}{7}e^{5} - \frac{1}{7}e^{4} + \frac{33}{7}e^{3} - 5e - \frac{6}{7}$
11 $[11, 11, 4w - 23]$ $-\frac{2}{7}e^{5} - \frac{4}{7}e^{4} + \frac{20}{7}e^{3} + 4e^{2} - 7e - \frac{24}{7}$
13 $[13, 13, -2w + 11]$ $\phantom{-}\frac{4}{7}e^{5} - \frac{6}{7}e^{4} - \frac{33}{7}e^{3} + 7e^{2} + 4e - \frac{36}{7}$
13 $[13, 13, 2w + 9]$ $-\frac{2}{7}e^{5} + \frac{3}{7}e^{4} + \frac{20}{7}e^{3} - 4e^{2} - 6e + \frac{18}{7}$
25 $[25, 5, -5]$ $\phantom{-}\frac{8}{7}e^{5} - \frac{5}{7}e^{4} - \frac{73}{7}e^{3} + 6e^{2} + 17e - \frac{51}{7}$
31 $[31, 31, 2w - 13]$ $-e^{2} + e + 1$
31 $[31, 31, -2w - 11]$ $-\frac{4}{7}e^{5} + \frac{6}{7}e^{4} + \frac{40}{7}e^{3} - 8e^{2} - 11e + \frac{43}{7}$
41 $[41, 41, -8w - 39]$ $\phantom{-}\frac{5}{7}e^{5} - \frac{4}{7}e^{4} - \frac{57}{7}e^{3} + 7e^{2} + 21e - \frac{66}{7}$
41 $[41, 41, 8w - 47]$ $\phantom{-}\frac{12}{7}e^{5} + \frac{3}{7}e^{4} - \frac{106}{7}e^{3} + 25e - \frac{31}{7}$
53 $[53, 53, -26w - 125]$ $-\frac{3}{7}e^{5} + \frac{1}{7}e^{4} + \frac{37}{7}e^{3} - 14e - \frac{43}{7}$
53 $[53, 53, 26w - 151]$ $\phantom{-}\frac{1}{7}e^{5} + \frac{2}{7}e^{4} - \frac{10}{7}e^{3} - e^{2} + 4e - \frac{37}{7}$
61 $[61, 61, -14w + 81]$ $\phantom{-}e^{4} - 7e^{2} + 6e + 4$
61 $[61, 61, -14w - 67]$ $\phantom{-}e^{5} - 10e^{3} + e^{2} + 21e - 4$
83 $[83, 83, 2w - 15]$ $-\frac{5}{7}e^{5} + \frac{4}{7}e^{4} + \frac{57}{7}e^{3} - 3e^{2} - 23e - \frac{4}{7}$
83 $[83, 83, -2w - 13]$ $-\frac{19}{7}e^{5} + \frac{11}{7}e^{4} + \frac{162}{7}e^{3} - 15e^{2} - 30e + \frac{52}{7}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
7 $[7,7,-6w - 29]$ $-1$