# Properties

 Base field $\Q(\sqrt{393})$ Weight [2, 2] Level norm 6 Level $[6,6,5w - 52]$ Label 2.2.393.1-6.2-f Dimension 7 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 $[6,6,5w - 52]$ Label 2.2.393.1-6.2-f Dimension 7 Is CM no Is base change no Parent newspace dimension 44

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$x^{7}$ $\mathstrut -\mathstrut 12x^{5}$ $\mathstrut -\mathstrut x^{4}$ $\mathstrut +\mathstrut 40x^{3}$ $\mathstrut +\mathstrut 6x^{2}$ $\mathstrut -\mathstrut 28x$ $\mathstrut -\mathstrut 8$
Norm Prime Eigenvalue
2 $[2, 2, -17w - 160]$ $-1$
2 $[2, 2, -17w + 177]$ $\phantom{-}e$
3 $[3, 3, -842w + 8767]$ $-1$
7 $[7, 7, -2w + 21]$ $\phantom{-}\frac{1}{2}e^{5} - 4e^{3} - \frac{1}{2}e^{2} + 6e + 1$
7 $[7, 7, 2w + 19]$ $-\frac{1}{4}e^{6} + 3e^{4} - \frac{3}{4}e^{3} - 10e^{2} + \frac{9}{2}e + 6$
13 $[13, 13, -12w - 113]$ $\phantom{-}\frac{1}{4}e^{6} - 2e^{4} - \frac{5}{4}e^{3} + 3e^{2} + \frac{11}{2}e - 1$
13 $[13, 13, 12w - 125]$ $\phantom{-}\frac{1}{4}e^{6} - 3e^{4} + \frac{3}{4}e^{3} + 10e^{2} - \frac{9}{2}e - 7$
17 $[17, 17, 182w - 1895]$ $-\frac{1}{4}e^{6} + 4e^{4} - \frac{3}{4}e^{3} - 16e^{2} + \frac{7}{2}e + 9$
17 $[17, 17, 182w + 1713]$ $-\frac{1}{4}e^{6} + \frac{1}{2}e^{5} + 3e^{4} - \frac{19}{4}e^{3} - \frac{19}{2}e^{2} + \frac{19}{2}e + 6$
23 $[23, 23, -512w - 4819]$ $\phantom{-}\frac{1}{4}e^{6} - 3e^{4} - \frac{1}{4}e^{3} + 11e^{2} + \frac{1}{2}e - 9$
23 $[23, 23, 512w - 5331]$ $\phantom{-}\frac{1}{2}e^{5} - 4e^{3} - \frac{1}{2}e^{2} + 8e + 1$
25 $[25, 5, -5]$ $-\frac{1}{2}e^{6} + \frac{1}{2}e^{5} + 5e^{4} - \frac{7}{2}e^{3} - \frac{27}{2}e^{2} + 5e + 9$
29 $[29, 29, 22w - 229]$ $\phantom{-}\frac{1}{2}e^{5} - 4e^{3} - \frac{1}{2}e^{2} + 4e + 4$
29 $[29, 29, 22w + 207]$ $\phantom{-}\frac{3}{4}e^{6} - \frac{1}{2}e^{5} - 9e^{4} + \frac{17}{4}e^{3} + \frac{57}{2}e^{2} - \frac{15}{2}e - 12$
43 $[43, 43, 114w + 1073]$ $\phantom{-}\frac{1}{2}e^{6} - \frac{1}{2}e^{5} - 4e^{4} + \frac{7}{2}e^{3} + \frac{17}{2}e^{2} - 5e - 13$
43 $[43, 43, 114w - 1187]$ $-\frac{1}{2}e^{6} + 5e^{4} + \frac{3}{2}e^{3} - 14e^{2} - 6e + 9$
47 $[47, 47, 8w - 83]$ $-\frac{1}{4}e^{6} + 3e^{4} - \frac{3}{4}e^{3} - 10e^{2} + \frac{5}{2}e + 10$
47 $[47, 47, -8w - 75]$ $\phantom{-}\frac{1}{4}e^{6} - 2e^{4} - \frac{1}{4}e^{3} + 2e^{2} - \frac{3}{2}e + 5$
61 $[61, 61, -1172w - 11031]$ $-\frac{1}{2}e^{6} + \frac{1}{2}e^{5} + 6e^{4} - \frac{9}{2}e^{3} - \frac{41}{2}e^{2} + 7e + 17$
61 $[61, 61, 1172w - 12203]$ $\phantom{-}\frac{1}{4}e^{6} + \frac{1}{2}e^{5} - 4e^{4} - \frac{13}{4}e^{3} + \frac{33}{2}e^{2} + \frac{3}{2}e - 12$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2,2,17w + 160]$ $1$
3 $[3,3,842w + 7925]$ $1$