Properties

 Base field $$\Q(\sqrt{53})$$ Weight [2, 2] Level norm 900 Level $[900, 30, -30]$ Label 2.2.53.1-900.1-f Dimension 1 CM no Base change yes

Related objects

Base field $$\Q(\sqrt{53})$$

Generator $$w$$, with minimal polynomial $$x^{2} - x - 13$$; narrow class number $$1$$ and class number $$1$$.

Form

 Weight [2, 2] Level $[900, 30, -30]$ Label 2.2.53.1-900.1-f Dimension 1 Is CM no Is base change yes Parent newspace dimension 9

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, 2]$ $\phantom{-}1$
7 $[7, 7, w + 2]$ $-4$
7 $[7, 7, w - 3]$ $-4$
9 $[9, 3, 3]$ $\phantom{-}1$
11 $[11, 11, w + 1]$ $\phantom{-}0$
11 $[11, 11, w - 2]$ $\phantom{-}0$
13 $[13, 13, w]$ $\phantom{-}2$
13 $[13, 13, w - 1]$ $\phantom{-}2$
17 $[17, 17, -w - 5]$ $\phantom{-}6$
17 $[17, 17, w - 6]$ $\phantom{-}6$
25 $[25, 5, -5]$ $\phantom{-}1$
29 $[29, 29, -w - 6]$ $-6$
29 $[29, 29, w - 7]$ $-6$
37 $[37, 37, 2w - 5]$ $\phantom{-}2$
37 $[37, 37, -2w - 3]$ $\phantom{-}2$
43 $[43, 43, -w - 7]$ $-4$
43 $[43, 43, w - 8]$ $-4$
47 $[47, 47, 3w + 7]$ $\phantom{-}0$
47 $[47, 47, 3w - 10]$ $\phantom{-}0$
53 $[53, 53, 2w - 1]$ $-6$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $-1$
9 $[9, 3, 3]$ $-1$
25 $[25, 5, -5]$ $-1$