Properties

 Label 4.4.14272.1-27.2-b Base field 4.4.14272.1 Weight $[2, 2, 2, 2]$ Level norm $27$ Level $[27, 27, w^{3} - 2w^{2} - 3w]$ Dimension $1$ CM no Base change no

Related objects

Base field 4.4.14272.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 5x^{2} + 2x + 3$$; narrow class number $$2$$ and class number $$1$$.

Form

 Weight: $[2, 2, 2, 2]$ Level: $[27, 27, w^{3} - 2w^{2} - 3w]$ Dimension: $1$ CM: no Base change: no Newspace dimension: $30$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}0$
4 $[4, 2, -w^{3} + 3w^{2} + w - 2]$ $\phantom{-}1$
11 $[11, 11, -w^{3} + 3w^{2} + 2w - 5]$ $-3$
13 $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ $\phantom{-}1$
13 $[13, 13, -w + 2]$ $-4$
17 $[17, 17, w^{3} - 3w^{2} - 2w + 2]$ $\phantom{-}3$
19 $[19, 19, -w^{2} + w + 4]$ $\phantom{-}8$
19 $[19, 19, w^{3} - 2w^{2} - 3w + 2]$ $-2$
23 $[23, 23, w^{2} - 2w - 1]$ $\phantom{-}6$
27 $[27, 3, w^{3} - 2w^{2} - 5w - 1]$ $-4$
29 $[29, 29, -w^{3} + 2w^{2} + 5w - 1]$ $\phantom{-}6$
37 $[37, 37, -w^{3} + 2w^{2} + 5w - 4]$ $-2$
41 $[41, 41, 2w^{3} - 5w^{2} - 6w + 4]$ $\phantom{-}0$
53 $[53, 53, w^{3} - 2w^{2} - 3w - 2]$ $\phantom{-}3$
59 $[59, 59, w - 4]$ $-6$
67 $[67, 67, 2w^{2} - 3w - 8]$ $\phantom{-}14$
73 $[73, 73, 2w^{3} - 5w^{2} - 6w + 5]$ $-11$
89 $[89, 89, -2w^{3} + 6w^{2} + 5w - 7]$ $\phantom{-}18$
97 $[97, 97, -2w^{3} + 6w^{2} + 3w - 7]$ $\phantom{-}14$
97 $[97, 97, -w^{3} + 3w^{2} + 3w - 1]$ $\phantom{-}10$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w]$ $1$