# Properties

 Base field $$\Q(\sqrt{109})$$ Weight [2, 2] Level norm 1 Level $[1, 1, 1]$ Label 2.2.109.1-1.1-b Dimension 3 CM no Base change yes

# Related objects

## 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 $[1, 1, 1]$ Label 2.2.109.1-1.1-b Dimension 3 Is CM no Is base change yes Parent newspace dimension 4

## Hecke eigenvalues ($q$-expansion)

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

## Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is $$(1)$$.