Properties

Label 3.3.1573.1-14.1-e
Base field 3.3.1573.1
Weight $[2, 2, 2]$
Level norm $14$
Level $[14, 14, -w^{2} + 4w - 2]$
Dimension $3$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 3.3.1573.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 2\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[14, 14, -w^{2} + 4w - 2]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $17$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} - 5x^{2} + 5x + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w]$ $-1$
4 $[4, 2, w^{2} - w - 7]$ $\phantom{-}e$
5 $[5, 5, w - 1]$ $-e^{2} + 2e + 3$
7 $[7, 7, w + 1]$ $\phantom{-}1$
11 $[11, 11, -w^{2} + 5]$ $\phantom{-}0$
13 $[13, 13, w + 3]$ $-2e + 4$
13 $[13, 13, -2w + 1]$ $\phantom{-}2e^{2} - 7e + 3$
19 $[19, 19, 2w^{2} - w - 15]$ $-e^{2} + 6e - 1$
25 $[25, 5, w^{2} - 7]$ $-2e^{2} + 6e + 4$
27 $[27, 3, 3]$ $-e^{2} - e + 8$
31 $[31, 31, w^{2} - 2w - 1]$ $\phantom{-}3e^{2} - 9e + 4$
37 $[37, 37, -3w^{2} + 2w + 23]$ $\phantom{-}3e^{2} - 10e - 1$
41 $[41, 41, -2w - 1]$ $-4e^{2} + 16e - 6$
47 $[47, 47, w^{2} - 3]$ $\phantom{-}2e^{2} - 3e - 9$
49 $[49, 7, w^{2} - 2w - 5]$ $-e^{2} + 4e + 1$
59 $[59, 59, 2w - 3]$ $-5e^{2} + 20e - 5$
67 $[67, 67, w - 5]$ $\phantom{-}3e^{2} - 13e + 2$
71 $[71, 71, w^{2} - 2w - 11]$ $-6e^{2} + 22e - 10$
73 $[73, 73, w^{2} + 1]$ $-4e^{2} + 14e - 6$
83 $[83, 83, -4w^{2} + 3w + 27]$ $\phantom{-}5e^{2} - 23e + 14$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w]$ $1$
$7$ $[7, 7, w + 1]$ $-1$