Properties

Label 4.4.16609.1-15.1-f
Base field 4.4.16609.1
Weight $[2, 2, 2, 2]$
Level norm $15$
Level $[15, 15, w^{3} - 5w - 3]$
Dimension $4$
CM no
Base change no

Related objects

Downloads

Learn more about

Base field 4.4.16609.1

Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} - x + 9\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[15, 15, w^{3} - 5w - 3]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $23$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} + 2x^{3} - 5x^{2} - 11x - 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + w + 4]$ $\phantom{-}e$
3 $[3, 3, -w^{2} + w + 3]$ $-1$
5 $[5, 5, w^{2} - 4]$ $\phantom{-}1$
8 $[8, 2, w^{3} - w^{2} - 4w + 5]$ $\phantom{-}2e^{3} + e^{2} - 11e - 9$
17 $[17, 17, -w^{2} + w + 5]$ $\phantom{-}e^{3} - e^{2} - 5e + 3$
27 $[27, 3, -w^{3} + 4w - 2]$ $\phantom{-}e^{3} + e^{2} - 4e - 10$
29 $[29, 29, -w^{2} + w + 1]$ $-e^{3} - 2e^{2} + 4e + 9$
29 $[29, 29, -w^{3} + 4w + 2]$ $-3e^{3} - 3e^{2} + 17e + 15$
37 $[37, 37, -2w^{3} + 3w^{2} + 9w - 13]$ $\phantom{-}e^{3} + 3e^{2} - 8e - 14$
41 $[41, 41, w^{3} - w^{2} - 5w + 2]$ $-e^{3} - 3e^{2} + 5e + 9$
43 $[43, 43, -w^{3} + w^{2} + 3w - 4]$ $-2e^{3} - e^{2} + 11e + 4$
61 $[61, 61, w^{2} - 2w - 2]$ $-2e^{3} + 10e - 2$
61 $[61, 61, 2w^{2} - w - 8]$ $\phantom{-}e^{3} + 3e^{2} - 4e - 14$
67 $[67, 67, -4w^{3} + 5w^{2} + 18w - 22]$ $\phantom{-}e^{3} + 3e^{2} - 10e - 14$
73 $[73, 73, -w^{2} - 2w + 2]$ $-3e^{3} + e^{2} + 12e - 4$
79 $[79, 79, w^{2} - 2w - 4]$ $-e^{3} + 4e + 5$
89 $[89, 89, w^{2} + w - 5]$ $-e^{3} - 2e^{2} + 3e + 6$
89 $[89, 89, 2w^{3} - 2w^{2} - 9w + 8]$ $-7e^{3} - 4e^{2} + 38e + 27$
89 $[89, 89, w^{3} - 5w - 5]$ $-e^{3} + 3e^{2} + 6e - 6$
89 $[89, 89, -w^{3} + 2w^{2} + 4w - 4]$ $\phantom{-}3e^{2} - 9$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, -w^{2} + w + 3]$ $1$
$5$ $[5, 5, w^{2} - 4]$ $-1$