Properties

Label 6.6.1259712.1-37.1-e
Base field \(\Q(\zeta_{36})^+\)
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $37$
Level $[37, 37, w^{4} - 5w^{2} - w + 5]$
Dimension $22$
CM no
Base change no

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Base field \(\Q(\zeta_{36})^+\)

Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} + 9x^{2} - 3\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[37, 37, w^{4} - 5w^{2} - w + 5]$
Dimension: $22$
CM: no
Base change: no
Newspace dimension: $30$

Hecke eigenvalues ($q$-expansion)

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

\(x^{22} - 50x^{20} + 1066x^{18} - 12665x^{16} + 92003x^{14} - 422173x^{12} + 1222435x^{10} - 2172392x^{8} + 2241113x^{6} - 1228148x^{4} + 322256x^{2} - 30976\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
8 $[8, 2, w^{3} - 3w - 1]$ $...$
37 $[37, 37, w^{4} - 5w^{2} - w + 5]$ $-1$
37 $[37, 37, w^{5} - 5w^{3} - w^{2} + 4w + 1]$ $...$
37 $[37, 37, -w^{5} + w^{4} + 5w^{3} - 4w^{2} - 5w + 1]$ $...$
37 $[37, 37, w^{5} + w^{4} - 5w^{3} - 4w^{2} + 5w + 1]$ $...$
37 $[37, 37, w^{5} - 5w^{3} + w^{2} + 4w - 1]$ $...$
37 $[37, 37, -w^{4} + 5w^{2} - w - 5]$ $...$
71 $[71, 71, w^{5} - 5w^{3} - w^{2} + 5w + 4]$ $...$
71 $[71, 71, w^{5} - 4w^{3} - w^{2} + w + 2]$ $...$
71 $[71, 71, w^{5} + w^{4} - 5w^{3} - 5w^{2} + 4w + 2]$ $...$
71 $[71, 71, w^{5} - w^{4} - 5w^{3} + 5w^{2} + 4w - 2]$ $...$
71 $[71, 71, -w^{5} + 4w^{3} - w^{2} - w + 2]$ $...$
71 $[71, 71, -w^{5} + 5w^{3} - w^{2} - 5w + 4]$ $...$
73 $[73, 73, w^{5} - 5w^{3} - w^{2} + 3w + 2]$ $...$
73 $[73, 73, 2w^{5} - w^{4} - 10w^{3} + 4w^{2} + 9w - 2]$ $...$
73 $[73, 73, -w^{5} + 4w^{3} - w^{2} - 2w + 2]$ $...$
73 $[73, 73, w^{5} - 4w^{3} - w^{2} + 2w + 2]$ $...$
73 $[73, 73, -2w^{5} - w^{4} + 10w^{3} + 4w^{2} - 9w - 2]$ $...$
73 $[73, 73, w^{5} - 5w^{3} + w^{2} + 3w - 2]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$37$ $[37, 37, w^{4} - 5w^{2} - w + 5]$ $1$