Properties

 Base field $$\Q(\sqrt{85})$$ Weight [2, 2] Level norm 15 Level $[15, 15, w + 2]$ Label 2.2.85.1-15.1-a Dimension 2 CM no Base change no

Related objects

• L-function not available

Base field $$\Q(\sqrt{85})$$

Generator $$w$$, with minimal polynomial $$x^{2} - x - 21$$; narrow class number $$2$$ and class number $$2$$.

Form

 Weight [2, 2] Level $[15, 15, w + 2]$ Label 2.2.85.1-15.1-a Dimension 2 Is CM no Is base change no Parent newspace dimension 30

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2} + 4$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $\phantom{-}\frac{1}{2}e$
4 $[4, 2, 2]$ $\phantom{-}1$
5 $[5, 5, w + 2]$ $\phantom{-}\frac{1}{2}e$
7 $[7, 7, w]$ $\phantom{-}2e$
7 $[7, 7, w + 6]$ $-2e$
17 $[17, 17, w + 8]$ $\phantom{-}3e$
19 $[19, 19, w + 1]$ $\phantom{-}2$
19 $[19, 19, w - 2]$ $-4$
23 $[23, 23, w + 9]$ $\phantom{-}0$
23 $[23, 23, w + 13]$ $\phantom{-}0$
37 $[37, 37, w + 11]$ $\phantom{-}4e$
37 $[37, 37, w + 25]$ $-e$
59 $[59, 59, 3w + 10]$ $\phantom{-}0$
59 $[59, 59, 3w - 13]$ $\phantom{-}12$
73 $[73, 73, w + 15]$ $-5e$
73 $[73, 73, w + 57]$ $-7e$
89 $[89, 89, -w - 10]$ $-6$
89 $[89, 89, w - 11]$ $\phantom{-}12$
97 $[97, 97, w + 22]$ $\phantom{-}5e$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 2]$ $-\frac{1}{2}e$
5 $[5, 5, w + 2]$ $-\frac{1}{2}e$