Properties

Label 3.3.1944.1-11.1-a
Base field 3.3.1944.1
Weight $[2, 2, 2]$
Level norm $11$
Level $[11, 11, w^{2} - w - 1]$
Dimension $27$
CM no
Base change no

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Base field 3.3.1944.1

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

Form

Weight: $[2, 2, 2]$
Level: $[11, 11, w^{2} - w - 1]$
Dimension: $27$
CM: no
Base change: no
Newspace dimension: $63$

Hecke eigenvalues ($q$-expansion)

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

\(x^{27} + 2x^{26} - 37x^{25} - 72x^{24} + 597x^{23} + 1131x^{22} - 5511x^{21} - 10172x^{20} + 32110x^{19} + 57766x^{18} - 123023x^{17} - 215462x^{16} + 313897x^{15} + 532452x^{14} - 531304x^{13} - 860574x^{12} + 588906x^{11} + 881679x^{10} - 419651x^{9} - 544806x^{8} + 183250x^{7} + 186546x^{6} - 42244x^{5} - 30334x^{4} + 2986x^{3} + 1751x^{2} + 137x + 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + 2w + 2]$ $\phantom{-}e$
2 $[2, 2, w + 1]$ $...$
3 $[3, 3, w^{2} - w - 9]$ $...$
7 $[7, 7, w^{2} - w - 7]$ $...$
11 $[11, 11, w^{2} - w - 1]$ $-1$
13 $[13, 13, -2w - 1]$ $...$
17 $[17, 17, -2w^{2} + 6w + 5]$ $...$
31 $[31, 31, -2w^{2} + 2w + 19]$ $...$
37 $[37, 37, 2w^{2} - 13]$ $...$
41 $[41, 41, w^{2} - w - 5]$ $...$
43 $[43, 43, 2w^{2} - 2w - 17]$ $...$
43 $[43, 43, -2w + 7]$ $...$
43 $[43, 43, 12w^{2} - 8w - 101]$ $...$
49 $[49, 7, w^{2} + w - 1]$ $...$
59 $[59, 59, -w^{2} + w + 11]$ $...$
61 $[61, 61, -w^{2} - w - 1]$ $...$
79 $[79, 79, -2w^{2} + 4w + 7]$ $...$
83 $[83, 83, 2w - 1]$ $...$
89 $[89, 89, 5w^{2} - 3w - 43]$ $...$
103 $[103, 103, -2w + 5]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$11$ $[11, 11, w^{2} - w - 1]$ $1$