Properties

Label 3.3.621.1-23.2-b
Base field 3.3.621.1
Weight $[2, 2, 2]$
Level norm $23$
Level $[23, 23, -w^{2} + 2]$
Dimension $17$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 3.3.621.1

Generator \(w\), with minimal polynomial \(x^{3} - 6x - 3\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[23, 23, -w^{2} + 2]$
Dimension: $17$
CM: no
Base change: no
Newspace dimension: $21$

Hecke eigenvalues ($q$-expansion)

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

\(x^{17} - 29x^{15} + x^{14} + 340x^{13} - 18x^{12} - 2066x^{11} + 110x^{10} + 6944x^{9} - 236x^{8} - 12802x^{7} - 36x^{6} + 12110x^{5} + 546x^{4} - 4941x^{3} - 376x^{2} + 495x - 27\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}e$
3 $[3, 3, w]$ $...$
4 $[4, 2, -w^{2} + w + 5]$ $...$
7 $[7, 7, -w + 2]$ $...$
19 $[19, 19, -2w^{2} + w + 10]$ $...$
23 $[23, 23, -w^{2} + 8]$ $...$
23 $[23, 23, -w^{2} + 2]$ $\phantom{-}1$
29 $[29, 29, -w^{2} + 2w + 4]$ $...$
37 $[37, 37, w^{2} - 2w - 8]$ $...$
41 $[41, 41, 4w^{2} - 3w - 20]$ $...$
43 $[43, 43, -w - 4]$ $...$
47 $[47, 47, 2w - 1]$ $...$
49 $[49, 7, -2w^{2} + 3w + 4]$ $...$
59 $[59, 59, 2w^{2} - 13]$ $...$
61 $[61, 61, -3w^{2} + 4w + 10]$ $...$
67 $[67, 67, 2w^{2} - 2w - 7]$ $...$
71 $[71, 71, -3w - 4]$ $...$
79 $[79, 79, 2w^{2} - 3w - 8]$ $...$
83 $[83, 83, 2w^{2} - w - 14]$ $...$
83 $[83, 83, -4w^{2} + 3w + 22]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$23$ $[23, 23, -w^{2} + 2]$ $-1$