Properties

Label 3.3.1345.1-29.1-b
Base field 3.3.1345.1
Weight $[2, 2, 2]$
Level norm $29$
Level $[29, 29, w^{2} - w - 3]$
Dimension $34$
CM no
Base change no

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Base field 3.3.1345.1

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

Form

Weight: $[2, 2, 2]$
Level: $[29, 29, w^{2} - w - 3]$
Dimension: $34$
CM: no
Base change: no
Newspace dimension: $56$

Hecke eigenvalues ($q$-expansion)

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

\(x^{34} - 105x^{32} + 18x^{31} + 4873x^{30} - 1548x^{29} - 131751x^{28} + 57295x^{27} + 2304481x^{26} - 1195900x^{25} - 27413354x^{24} + 15494330x^{23} + 227319030x^{22} - 129176773x^{21} - 1327859115x^{20} + 693762380x^{19} + 5471819775x^{18} - 2320080860x^{17} - 15814233323x^{16} + 4350835162x^{15} + 31568403187x^{14} - 2801664301x^{13} - 42109871720x^{12} - 4771188687x^{11} + 35185703403x^{10} + 10979968878x^{9} - 16229359650x^{8} - 8369299713x^{7} + 2909489716x^{6} + 2514822300x^{5} + 167346368x^{4} - 165661293x^{3} - 23631172x^{2} + 3130302x + 516411\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -w - 1]$ $\phantom{-}e$
5 $[5, 5, w + 2]$ $...$
7 $[7, 7, w + 3]$ $...$
7 $[7, 7, -w + 2]$ $...$
7 $[7, 7, -w + 1]$ $...$
8 $[8, 2, 2]$ $...$
13 $[13, 13, -w^{2} + w + 4]$ $...$
19 $[19, 19, -w^{2} + 5]$ $...$
23 $[23, 23, -w^{2} - w + 3]$ $...$
27 $[27, 3, 3]$ $...$
29 $[29, 29, w^{2} - w - 3]$ $\phantom{-}1$
31 $[31, 31, w^{2} - w - 8]$ $...$
37 $[37, 37, -w - 4]$ $...$
43 $[43, 43, 2w^{2} - 4w - 3]$ $...$
47 $[47, 47, w^{2} - 3]$ $...$
53 $[53, 53, 2w^{2} - w - 11]$ $...$
59 $[59, 59, w^{2} - 2w - 4]$ $...$
67 $[67, 67, w^{2} + w - 8]$ $...$
71 $[71, 71, w^{2} + w - 11]$ $...$
73 $[73, 73, -w^{2} + 4w - 2]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$29$ $[29, 29, w^{2} - w - 3]$ $-1$