Properties

Label 3.3.1708.1-7.1-b
Base field 3.3.1708.1
Weight $[2, 2, 2]$
Level norm $7$
Level $[7, 7, -2w^{2} + 2w + 17]$
Dimension $21$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 3.3.1708.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x - 2\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[7, 7, -2w^{2} + 2w + 17]$
Dimension: $21$
CM: no
Base change: no
Newspace dimension: $31$

Hecke eigenvalues ($q$-expansion)

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

\(x^{21} - 4x^{20} - 27x^{19} + 117x^{18} + 301x^{17} - 1440x^{16} - 1810x^{15} + 9739x^{14} + 6480x^{13} - 39572x^{12} - 14680x^{11} + 98995x^{10} + 22686x^{9} - 149796x^{8} - 25612x^{7} + 128722x^{6} + 18992x^{5} - 54768x^{4} - 6032x^{3} + 8456x^{2} - 64x - 96\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}e$
2 $[2, 2, w^{2} - 2w - 5]$ $...$
5 $[5, 5, w^{2} + 3w + 1]$ $...$
7 $[7, 7, -2w^{2} + 2w + 17]$ $\phantom{-}1$
7 $[7, 7, -w^{2} + w + 9]$ $...$
13 $[13, 13, 2w + 1]$ $...$
25 $[25, 5, -3w^{2} + 5w + 19]$ $...$
27 $[27, 3, 3]$ $...$
29 $[29, 29, w^{2} + w - 1]$ $...$
31 $[31, 31, w^{2} - w - 1]$ $...$
37 $[37, 37, 2w^{2} + 6w + 3]$ $...$
41 $[41, 41, -6w^{2} - 14w - 3]$ $...$
53 $[53, 53, -4w^{2} + 6w + 27]$ $...$
59 $[59, 59, 2w^{2} - 4w - 11]$ $...$
61 $[61, 61, w^{2} - w - 3]$ $...$
61 $[61, 61, -2w^{2} + 2w + 13]$ $...$
73 $[73, 73, w^{2} + 3w + 3]$ $...$
97 $[97, 97, w^{2} + w - 15]$ $...$
101 $[101, 101, w^{2} + 3w - 1]$ $...$
101 $[101, 101, w^{2} - w - 11]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$7$ $[7, 7, -2w^{2} + 2w + 17]$ $-1$