# Properties

 Base field $\Q(\sqrt{393})$ Weight [2, 2] Level norm 4 Level $[4, 2, 2]$ Label 2.2.393.1-4.1-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 $[4, 2, 2]$ Label 2.2.393.1-4.1-a Dimension 2 Is CM no Is base change no Parent newspace dimension 36

## Hecke eigenvalues ($q$-expansion)

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

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -17w - 160]$ $-1$
2 $[2, 2, -17w + 177]$ $1$