Properties

 Base field $$\Q(\sqrt{109})$$ Weight [2, 2] Level norm 12 Level $[12, 6, -2w + 12]$ Label 2.2.109.1-12.1-h Dimension 3 CM no Base change no

Related objects

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Base field $$\Q(\sqrt{109})$$

Generator $$w$$, with minimal polynomial $$x^{2} - x - 27$$; narrow class number $$1$$ and class number $$1$$.

Form

 Weight [2, 2] Level $[12, 6, -2w + 12]$ Label 2.2.109.1-12.1-h Dimension 3 Is CM no Is base change no Parent newspace dimension 14

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{3}$$ $$\mathstrut -\mathstrut 3x^{2}$$ $$\mathstrut -\mathstrut x$$ $$\mathstrut +\mathstrut 2$$
Norm Prime Eigenvalue
3 $[3, 3, -w + 6]$ $-1$
3 $[3, 3, w + 5]$ $\phantom{-}e$
4 $[4, 2, 2]$ $-1$
5 $[5, 5, -3w + 17]$ $\phantom{-}e^{2} - 3e + 1$
5 $[5, 5, -3w - 14]$ $-e^{2} + 2e$
7 $[7, 7, w - 5]$ $\phantom{-}2e^{2} - 5e - 2$
7 $[7, 7, w + 4]$ $\phantom{-}e + 1$
29 $[29, 29, -w - 7]$ $\phantom{-}2e - 2$
29 $[29, 29, -w + 8]$ $-e^{2} + 6$
31 $[31, 31, -5w + 28]$ $-2e^{2} + 4e + 4$
31 $[31, 31, -5w - 23]$ $\phantom{-}e^{2} + e - 3$
43 $[43, 43, 6w + 29]$ $\phantom{-}e + 4$
43 $[43, 43, -6w + 35]$ $\phantom{-}e^{2} - 8e + 5$
61 $[61, 61, 3w - 19]$ $\phantom{-}2$
61 $[61, 61, -3w - 16]$ $-4e^{2} + 10e$
71 $[71, 71, -7w - 34]$ $\phantom{-}e^{2} + 5$
71 $[71, 71, 7w - 41]$ $\phantom{-}e^{2} - e + 1$
73 $[73, 73, 2w - 7]$ $-2e + 2$
73 $[73, 73, -2w - 5]$ $\phantom{-}10$
83 $[83, 83, -w - 10]$ $-5e^{2} + 13e + 1$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w + 6]$ $1$
4 $[4, 2, 2]$ $1$