# Properties

 Base field $$\Q(\sqrt{113})$$ Weight [2, 2] Level norm 9 Level $[9, 3, 3]$ Label 2.2.113.1-9.1-d Dimension 4 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 $[9, 3, 3]$ Label 2.2.113.1-9.1-d Dimension 4 Is CM no Is base change no Parent newspace dimension 24

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4}$$ $$\mathstrut +\mathstrut x^{3}$$ $$\mathstrut -\mathstrut 8x^{2}$$ $$\mathstrut -\mathstrut 6x$$ $$\mathstrut +\mathstrut 11$$
Norm Prime Eigenvalue
2 $[2, 2, -w + 6]$ $\phantom{-}e$
2 $[2, 2, w + 5]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{8}{3}e - \frac{1}{3}$
7 $[7, 7, 6w - 35]$ $-\frac{2}{3}e^{3} + e^{2} + \frac{13}{3}e - \frac{10}{3}$
7 $[7, 7, -6w - 29]$ $-e^{2} - e + 5$
9 $[9, 3, 3]$ $-1$
11 $[11, 11, 4w + 19]$ $\phantom{-}\frac{2}{3}e^{3} - e^{2} - \frac{10}{3}e + \frac{16}{3}$
11 $[11, 11, 4w - 23]$ $\phantom{-}\frac{1}{3}e^{3} + e^{2} - \frac{5}{3}e - \frac{10}{3}$
13 $[13, 13, -2w + 11]$ $\phantom{-}\frac{1}{3}e^{3} - e^{2} + \frac{1}{3}e + \frac{20}{3}$
13 $[13, 13, 2w + 9]$ $\phantom{-}\frac{2}{3}e^{3} + e^{2} - \frac{16}{3}e - \frac{8}{3}$
25 $[25, 5, -5]$ $\phantom{-}e^{3} - 5e + 1$
31 $[31, 31, 2w - 13]$ $-\frac{4}{3}e^{3} + e^{2} + \frac{26}{3}e - \frac{5}{3}$
31 $[31, 31, -2w - 11]$ $-\frac{1}{3}e^{3} - e^{2} - \frac{1}{3}e + \frac{19}{3}$
41 $[41, 41, -8w - 39]$ $-e^{3} - e^{2} + 6e - 1$
41 $[41, 41, 8w - 47]$ $-e^{3} + e^{2} + 4e - 10$
53 $[53, 53, -26w - 125]$ $-\frac{5}{3}e^{3} + \frac{22}{3}e + \frac{2}{3}$
53 $[53, 53, 26w - 151]$ $-2e^{3} + 11e + 1$
61 $[61, 61, -14w + 81]$ $\phantom{-}\frac{2}{3}e^{3} + e^{2} - \frac{16}{3}e - \frac{11}{3}$
61 $[61, 61, -14w - 67]$ $\phantom{-}\frac{1}{3}e^{3} - e^{2} + \frac{1}{3}e + \frac{17}{3}$
83 $[83, 83, 2w - 15]$ $\phantom{-}\frac{1}{3}e^{3} + 3e^{2} - \frac{8}{3}e - \frac{37}{3}$
83 $[83, 83, -2w - 13]$ $\phantom{-}e^{3} - 3e^{2} - 4e + 14$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, 3]$ $1$