# Properties

 Base field $$\Q(\sqrt{197})$$ Weight [2, 2] Level norm 23 Level $[23,23,-w + 9]$ Label 2.2.197.1-23.2-b Dimension 3 CM no Base change no

# Related objects

• L-function not available

## Base field $$\Q(\sqrt{197})$$

Generator $$w$$, with minimal polynomial $$x^{2} - x - 49$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2] Level $[23,23,-w + 9]$ Label 2.2.197.1-23.2-b Dimension 3 Is CM no Is base change no Parent newspace dimension 81

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{3}$$ $$\mathstrut -\mathstrut x^{2}$$ $$\mathstrut -\mathstrut 6x$$ $$\mathstrut +\mathstrut 4$$
Norm Prime Eigenvalue
4 $[4, 2, 2]$ $\phantom{-}e$
7 $[7, 7, w - 7]$ $\phantom{-}\frac{1}{2}e^{2} + \frac{1}{2}e - 2$
7 $[7, 7, w + 6]$ $-\frac{1}{2}e^{2} - \frac{1}{2}e + 4$
9 $[9, 3, 3]$ $-\frac{1}{2}e^{2} - \frac{1}{2}e + 2$
19 $[19, 19, w + 5]$ $-\frac{3}{2}e^{2} + \frac{1}{2}e + 2$
19 $[19, 19, w - 6]$ $-e - 2$
23 $[23, 23, w + 8]$ $\phantom{-}e^{2} - e - 2$
23 $[23, 23, -w + 9]$ $\phantom{-}1$
25 $[25, 5, 5]$ $\phantom{-}e^{2} - 2e - 5$
29 $[29, 29, -w - 4]$ $-2e^{2} + 5$
29 $[29, 29, w - 5]$ $\phantom{-}e^{2} - 2e$
37 $[37, 37, -w - 3]$ $\phantom{-}2e^{2} + 2e - 11$
37 $[37, 37, w - 4]$ $-\frac{1}{2}e^{2} + \frac{1}{2}e + 7$
41 $[41, 41, -w - 9]$ $\phantom{-}e^{2} + e - 1$
41 $[41, 41, w - 10]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{3}{2}e - 4$
43 $[43, 43, -w - 2]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 5$
43 $[43, 43, w - 3]$ $-6$
47 $[47, 47, -w - 1]$ $-e^{2} + 10$
47 $[47, 47, w - 2]$ $-\frac{3}{2}e^{2} + \frac{3}{2}e + 5$
53 $[53, 53, 2w - 13]$ $-\frac{3}{2}e^{2} + \frac{7}{2}e + 12$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
23 $[23,23,-w + 9]$ $-1$