Properties

 Label 4.4.11661.1-9.2-b Base field 4.4.11661.1 Weight $[2, 2, 2, 2]$ Level norm $9$ Level $[9, 3, -w^{2} + w + 3]$ Dimension $4$ CM no Base change yes

Related objects

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Base field 4.4.11661.1

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

Form

 Weight: $[2, 2, 2, 2]$ Level: $[9, 3, -w^{2} + w + 3]$ Dimension: $4$ CM: no Base change: yes Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

 $$x^{4} + x^{3} - 11x^{2} - 4x + 16$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}1$
3 $[3, 3, w - 2]$ $\phantom{-}e$
3 $[3, 3, w - 1]$ $\phantom{-}1$
16 $[16, 2, 2]$ $\phantom{-}e^{2} + e - 3$
23 $[23, 23, -w^{3} + 4w + 1]$ $-e^{3} - e^{2} + 7e + 4$
25 $[25, 5, w^{3} - 2w^{2} - 2w + 2]$ $-e^{2} + 6$
25 $[25, 5, w^{3} - w^{2} - 3w + 1]$ $-e^{2} + 6$
29 $[29, 29, w^{3} - 2w^{2} - 4w + 4]$ $-2e + 2$
29 $[29, 29, w^{3} - w^{2} - 5w + 1]$ $-2e + 2$
43 $[43, 43, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}e^{3} + e^{2} - 8e - 4$
43 $[43, 43, w^{3} - w^{2} - 4w + 2]$ $\phantom{-}e^{3} + e^{2} - 8e - 4$
61 $[61, 61, -w^{2} + 2w + 4]$ $-e^{3} - e^{2} + 8e + 2$
61 $[61, 61, w^{2} - 5]$ $-e^{3} - e^{2} + 8e + 2$
79 $[79, 79, 3w^{3} - 7w^{2} - 8w + 16]$ $\phantom{-}e^{2} - 8$
79 $[79, 79, -w^{3} + w^{2} + 6w - 4]$ $\phantom{-}e^{2} - 8$
101 $[101, 101, -w^{3} + 3w^{2} + w - 7]$ $-6$
101 $[101, 101, w^{3} - 4w - 4]$ $-6$
103 $[103, 103, 2w^{3} - w^{2} - 8w - 1]$ $-3e^{2} - 2e + 16$
103 $[103, 103, 2w^{3} - 5w^{2} - 4w + 8]$ $-3e^{2} - 2e + 16$
107 $[107, 107, 2w^{2} - 3w - 4]$ $-2e^{2} - 4e + 12$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

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