Properties

 Base field $$\Q(\sqrt{55})$$ Weight [2, 2] Level norm 5 Level $[5, 5, -2w + 15]$ Label 2.2.220.1-5.1-g Dimension 4 CM no Base change no

Related objects

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Base field $$\Q(\sqrt{55})$$

Generator $$w$$, with minimal polynomial $$x^{2} - 55$$; narrow class number $$4$$ and class number $$2$$.

Form

 Weight [2, 2] Level $[5, 5, -2w + 15]$ Label 2.2.220.1-5.1-g Dimension 4 Is CM no Is base change no Parent newspace dimension 60

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4}$$ $$\mathstrut +\mathstrut 8x^{2}$$ $$\mathstrut +\mathstrut 4$$
Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}\frac{1}{2}e^{3} + 3e$
3 $[3, 3, w + 1]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $-\frac{1}{2}e^{3} - 4e$
5 $[5, 5, -2w + 15]$ $-1$
11 $[11, 11, 3w - 22]$ $\phantom{-}2$
13 $[13, 13, w + 4]$ $-e^{3} - 9e$
13 $[13, 13, w + 9]$ $\phantom{-}\frac{1}{2}e^{3} + 6e$
17 $[17, 17, w + 2]$ $\phantom{-}e$
17 $[17, 17, w + 15]$ $-\frac{1}{2}e^{3} - 4e$
19 $[19, 19, -w - 6]$ $-e^{2}$
19 $[19, 19, w - 6]$ $\phantom{-}e^{2} + 8$
23 $[23, 23, w + 3]$ $-e^{3} - 5e$
23 $[23, 23, w + 20]$ $-\frac{3}{2}e^{3} - 10e$
47 $[47, 47, w + 14]$ $\phantom{-}2e^{3} + 13e$
47 $[47, 47, w + 33]$ $\phantom{-}\frac{3}{2}e^{3} + 8e$
49 $[49, 7, -7]$ $\phantom{-}2$
67 $[67, 67, w + 16]$ $-\frac{1}{2}e^{3} - 8e$
67 $[67, 67, w + 51]$ $\phantom{-}2e^{3} + 17e$
73 $[73, 73, w + 36]$ $-\frac{5}{2}e^{3} - 14e$
73 $[73, 73, w + 37]$ $-3e^{3} - 19e$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -2w + 15]$ $1$