Properties

 Base field $\Q(\sqrt{393})$ Weight [2, 2] Level norm 6 Level $[6, 6, -5w - 47]$ Label 2.2.393.1-6.1-d Dimension 3 CM no Base change no

Related objects

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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 $[6, 6, -5w - 47]$ Label 2.2.393.1-6.1-d Dimension 3 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:
$x^{3}$ $\mathstrut +\mathstrut x^{2}$ $\mathstrut -\mathstrut 2x$ $\mathstrut -\mathstrut 1$
Norm Prime Eigenvalue
2 $[2, 2, -17w - 160]$ $\phantom{-}e$
2 $[2, 2, -17w + 177]$ $\phantom{-}1$
3 $[3, 3, -842w + 8767]$ $-1$
7 $[7, 7, -2w + 21]$ $\phantom{-}1$
7 $[7, 7, 2w + 19]$ $-e - 2$
13 $[13, 13, -12w - 113]$ $\phantom{-}2e^{2} - 1$
13 $[13, 13, 12w - 125]$ $\phantom{-}e^{2} + 2e + 1$
17 $[17, 17, 182w - 1895]$ $-2e^{2} + 2e + 7$
17 $[17, 17, 182w + 1713]$ $-3e^{2} - e + 2$
23 $[23, 23, -512w - 4819]$ $\phantom{-}e^{2} - 4e - 6$
23 $[23, 23, 512w - 5331]$ $-e^{2} + e - 3$
25 $[25, 5, -5]$ $\phantom{-}2e^{2} - 2$
29 $[29, 29, 22w - 229]$ $-2e^{2} + 2$
29 $[29, 29, 22w + 207]$ $-5e^{2} - 5e + 7$
43 $[43, 43, 114w + 1073]$ $\phantom{-}6e^{2} + 5e - 6$
43 $[43, 43, 114w - 1187]$ $-2e^{2} - 2e + 6$
47 $[47, 47, 8w - 83]$ $\phantom{-}3e^{2} + 9e - 3$
47 $[47, 47, -8w - 75]$ $-e^{2} - 5e - 3$
61 $[61, 61, -1172w - 11031]$ $\phantom{-}8e^{2} + 6e - 12$
61 $[61, 61, 1172w - 12203]$ $\phantom{-}3e^{2} - 4e - 10$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -17w + 177]$ $-1$
3 $[3, 3, -842w + 8767]$ $1$