Properties

 Base field $\Q(\sqrt{67})$ Weight [2, 2] Level norm 9 Level $[9, 9, 16w + 131]$ Label 2.2.268.1-9.2-d Dimension 2 CM no Base change no

Related objects

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Base field $\Q(\sqrt{67})$

Generator $w$, with minimal polynomial $x^{2} - 67$; narrow class number $2$ and class number $1$.

Form

 Weight [2, 2] Level $[9, 9, 16w + 131]$ Label 2.2.268.1-9.2-d Dimension 2 Is CM no Is base change no Parent newspace dimension 48

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$x^{2}$ $\mathstrut +\mathstrut x$ $\mathstrut -\mathstrut 3$
Norm Prime Eigenvalue
2 $[2, 2, -27w + 221]$ $\phantom{-}0$
3 $[3, 3, -w + 8]$ $\phantom{-}e$
3 $[3, 3, -w - 8]$ $\phantom{-}0$
7 $[7, 7, -11w + 90]$ $-e - 3$
7 $[7, 7, -11w - 90]$ $-e - 3$
11 $[11, 11, 6w - 49]$ $\phantom{-}3$
11 $[11, 11, 6w + 49]$ $-3$
17 $[17, 17, 4w + 33]$ $\phantom{-}2e + 2$
17 $[17, 17, -4w + 33]$ $-2e - 2$
25 $[25, 5, -5]$ $-1$
29 $[29, 29, -70w + 573]$ $\phantom{-}2e + 5$
29 $[29, 29, 151w - 1236]$ $-2e - 5$
31 $[31, 31, -w - 6]$ $\phantom{-}2e + 3$
31 $[31, 31, w - 6]$ $\phantom{-}2e + 3$
37 $[37, 37, -21w - 172]$ $\phantom{-}e - 3$
37 $[37, 37, -21w + 172]$ $\phantom{-}e - 3$
43 $[43, 43, 2w - 15]$ $-e + 6$
43 $[43, 43, 2w + 15]$ $-e + 6$
67 $[67, 67, -w]$ $\phantom{-}2e + 12$
73 $[73, 73, -3w - 26]$ $-2e - 6$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w - 8]$ $-1$