Properties

 Label 4.4.11324.1-20.1-b Base field 4.4.11324.1 Weight $[2, 2, 2, 2]$ Level norm $20$ Level $[20, 10, -w^{3} + 4w - 2]$ Dimension $3$ CM no Base change no

Related objects

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Base field 4.4.11324.1

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

Form

 Weight: $[2, 2, 2, 2]$ Level: $[20, 10, -w^{3} + 4w - 2]$ Dimension: $3$ CM: no Base change: no Newspace dimension: $4$

Hecke eigenvalues ($q$-expansion)

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

 $$x^{3} + x^{2} - 8x - 4$$
Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}0$
4 $[4, 2, -w^{3} + 4w + 1]$ $\phantom{-}e$
5 $[5, 5, w + 1]$ $\phantom{-}1$
13 $[13, 13, -w^{2} + 3]$ $-e + 1$
17 $[17, 17, -w^{3} + w^{2} + 3w - 1]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{3}{2}e - 2$
19 $[19, 19, -w^{3} + 3w - 1]$ $-\frac{1}{2}e^{2} - \frac{1}{2}e + 6$
23 $[23, 23, -w + 3]$ $\phantom{-}e + 1$
31 $[31, 31, -w^{2} - 2w + 1]$ $-e^{2} + e + 6$
41 $[41, 41, w^{3} + w^{2} - 5w - 3]$ $\phantom{-}2e^{2} - 12$
43 $[43, 43, 2w - 1]$ $\phantom{-}e^{2} + 4e - 5$
53 $[53, 53, -w - 3]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{3}{2}e - 10$
53 $[53, 53, w^{3} - w^{2} - 4w + 1]$ $-e^{2} - e + 14$
61 $[61, 61, w^{3} - 3w - 5]$ $\phantom{-}e^{2} - e - 4$
67 $[67, 67, w^{3} + w^{2} - 5w - 1]$ $-\frac{1}{2}e^{2} - \frac{5}{2}e$
81 $[81, 3, -3]$ $-e^{2} - e + 6$
83 $[83, 83, -w^{3} + 5w - 3]$ $-3e^{2} - e + 18$
89 $[89, 89, w^{2} + 1]$ $\phantom{-}\frac{3}{2}e^{2} + \frac{3}{2}e - 8$
97 $[97, 97, w^{3} - w^{2} - 5w + 1]$ $-e^{2} - 3e$
97 $[97, 97, 3w^{3} - 5w^{2} - 14w + 21]$ $-e^{2} - e + 6$
97 $[97, 97, w^{3} - 3w - 3]$ $-e + 9$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

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