Properties

Label 6.6.980125.1-61.1-b
Base field 6.6.980125.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $61$
Level $[61, 61, -w^{4} + 4w^{2} - 2w - 2]$
Dimension $17$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 6.6.980125.1

Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 6x^{3} + 7x^{2} - 5x - 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[61, 61, -w^{4} + 4w^{2} - 2w - 2]$
Dimension: $17$
CM: no
Base change: no
Newspace dimension: $34$

Hecke eigenvalues ($q$-expansion)

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

\(x^{17} + 18x^{16} + 72x^{15} - 528x^{14} - 4869x^{13} - 4200x^{12} + 71550x^{11} + 210870x^{10} - 272888x^{9} - 1837806x^{8} - 974515x^{7} + 5372788x^{6} + 6908039x^{5} - 3063296x^{4} - 6316613x^{3} + 262498x^{2} + 739187x - 86528\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, -w^{2} + 2]$ $\phantom{-}e$
11 $[11, 11, w^{4} + w^{3} - 4w^{2} - 3w + 2]$ $...$
11 $[11, 11, -w^{5} + 6w^{3} - w^{2} - 7w + 1]$ $...$
19 $[19, 19, -w^{5} - w^{4} + 5w^{3} + 4w^{2} - 5w - 3]$ $...$
29 $[29, 29, -2w^{4} - w^{3} + 9w^{2} + 2w - 5]$ $...$
31 $[31, 31, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 7w + 1]$ $...$
41 $[41, 41, 2w^{5} + w^{4} - 10w^{3} - 3w^{2} + 7w + 2]$ $...$
41 $[41, 41, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 6w - 3]$ $...$
41 $[41, 41, w^{5} - 6w^{3} + w^{2} + 7w - 2]$ $...$
59 $[59, 59, -w^{5} - w^{4} + 4w^{3} + 4w^{2} - 2w - 3]$ $...$
59 $[59, 59, w^{5} - w^{4} - 5w^{3} + 6w^{2} + 2w - 4]$ $...$
59 $[59, 59, -w^{5} + 4w^{3} - w^{2} - w + 1]$ $...$
61 $[61, 61, -w^{4} + 4w^{2} - 2w - 2]$ $\phantom{-}1$
64 $[64, 2, -2]$ $...$
71 $[71, 71, 2w^{5} + w^{4} - 10w^{3} - 3w^{2} + 9w + 3]$ $...$
81 $[81, 3, w^{5} + 2w^{4} - 4w^{3} - 8w^{2} + 2w + 3]$ $...$
89 $[89, 89, -w^{5} + 6w^{3} - 7w]$ $...$
89 $[89, 89, w^{5} + w^{4} - 5w^{3} - 4w^{2} + 6w + 2]$ $...$
101 $[101, 101, w^{5} - 4w^{3} + 2w^{2} + w - 3]$ $...$
101 $[101, 101, w^{5} + 2w^{4} - 4w^{3} - 8w^{2} + 3w + 4]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$61$ $[61, 61, -w^{4} + 4w^{2} - 2w - 2]$ $-1$