# Properties

 Base field $\Q(\sqrt{393})$ Weight [2, 2] Level norm 3 Level $[3, 3, -842w + 8767]$ Label 2.2.393.1-3.1-a Dimension 2 CM no Base change no

# Related objects

• L-function not available

## Base field $\Q(\sqrt{393})$

Generator $w$, with minimal polynomial $x^{2} - x - 98$; narrow class number $2$ and class number $1$.

## Form

 Weight [2, 2] Level $[3, 3, -842w + 8767]$ Label 2.2.393.1-3.1-a Dimension 2 Is CM no Is base change no Parent newspace dimension 42

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$x^{2}$ $\mathstrut -\mathstrut 5$
Norm Prime Eigenvalue
2 $[2, 2, -17w - 160]$ $\phantom{-}0$
2 $[2, 2, -17w + 177]$ $\phantom{-}e$
3 $[3, 3, -842w + 8767]$ $-1$
7 $[7, 7, -2w + 21]$ $-3$
7 $[7, 7, 2w + 19]$ $\phantom{-}2$
13 $[13, 13, -12w - 113]$ $-4$
13 $[13, 13, 12w - 125]$ $\phantom{-}6$
17 $[17, 17, 182w - 1895]$ $\phantom{-}2e$
17 $[17, 17, 182w + 1713]$ $\phantom{-}2e$
23 $[23, 23, -512w - 4819]$ $\phantom{-}0$
23 $[23, 23, 512w - 5331]$ $\phantom{-}2e$
25 $[25, 5, -5]$ $\phantom{-}4$
29 $[29, 29, 22w - 229]$ $-2e$
29 $[29, 29, 22w + 207]$ $-e$
43 $[43, 43, 114w + 1073]$ $\phantom{-}1$
43 $[43, 43, 114w - 1187]$ $\phantom{-}6$
47 $[47, 47, 8w - 83]$ $\phantom{-}4e$
47 $[47, 47, -8w - 75]$ $-5e$
61 $[61, 61, -1172w - 11031]$ $\phantom{-}8$
61 $[61, 61, 1172w - 12203]$ $-2$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -842w + 8767]$ $1$