Properties

 Label 4.4.11661.1-1.1-a Base field 4.4.11661.1 Weight $[2, 2, 2, 2]$ Level norm $1$ Level $[1, 1, 1]$ Dimension $4$ CM no Base change yes

Related objects

• L-function not available

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: $[1, 1, 1]$ Dimension: $4$ CM: no Base change: yes Newspace dimension: $4$

Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - 12x^{2} + 8$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}\frac{1}{4}e^{3} - 3e$
3 $[3, 3, w - 2]$ $\phantom{-}e$
3 $[3, 3, w - 1]$ $\phantom{-}\frac{1}{4}e^{3} - 3e$
16 $[16, 2, 2]$ $-\frac{1}{2}e^{2} + 7$
23 $[23, 23, -w^{3} + 4w + 1]$ $\phantom{-}e^{2} - 10$
25 $[25, 5, w^{3} - 2w^{2} - 2w + 2]$ $-e^{3} + 9e$
25 $[25, 5, w^{3} - w^{2} - 3w + 1]$ $-e^{3} + 9e$
29 $[29, 29, w^{3} - 2w^{2} - 4w + 4]$ $\phantom{-}\frac{1}{4}e^{3} - e$
29 $[29, 29, w^{3} - w^{2} - 5w + 1]$ $\phantom{-}\frac{1}{4}e^{3} - e$
43 $[43, 43, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}\frac{1}{2}e^{2}$
43 $[43, 43, w^{3} - w^{2} - 4w + 2]$ $\phantom{-}\frac{1}{2}e^{2}$
61 $[61, 61, -w^{2} + 2w + 4]$ $\phantom{-}\frac{1}{2}e^{3} - 6e$
61 $[61, 61, w^{2} - 5]$ $\phantom{-}\frac{1}{2}e^{3} - 6e$
79 $[79, 79, 3w^{3} - 7w^{2} - 8w + 16]$ $\phantom{-}\frac{3}{4}e^{3} - 10e$
79 $[79, 79, -w^{3} + w^{2} + 6w - 4]$ $\phantom{-}\frac{3}{4}e^{3} - 10e$
101 $[101, 101, -w^{3} + 3w^{2} + w - 7]$ $-\frac{1}{2}e^{3} + 2e$
101 $[101, 101, w^{3} - 4w - 4]$ $-\frac{1}{2}e^{3} + 2e$
103 $[103, 103, 2w^{3} - w^{2} - 8w - 1]$ $\phantom{-}\frac{1}{2}e^{2} + 6$
103 $[103, 103, 2w^{3} - 5w^{2} - 4w + 8]$ $\phantom{-}\frac{1}{2}e^{2} + 6$
107 $[107, 107, 2w^{2} - 3w - 4]$ $-2e^{2} + 14$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is $$(1)$$.