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Properties

Label 29.3
Level 29
Weight 3
Dimension 56
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 210
Trace bound 1

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Defining parameters

Level: \( N \) = \( 29 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(210\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(29))\).

Total New Old
Modular forms 84 84 0
Cusp forms 56 56 0
Eisenstein series 28 28 0

Trace form

\( 56 q - 14 q^{2} - 14 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 14 q^{7} - 14 q^{8} - 14 q^{9} + O(q^{10}) \) \( 56 q - 14 q^{2} - 14 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 14 q^{7} - 14 q^{8} - 14 q^{9} - 14 q^{10} - 14 q^{11} - 14 q^{12} - 14 q^{13} - 14 q^{14} - 14 q^{15} - 14 q^{16} - 14 q^{17} - 14 q^{18} - 14 q^{19} + 154 q^{20} + 182 q^{21} + 154 q^{22} + 56 q^{23} + 322 q^{24} + 70 q^{25} + 56 q^{26} + 28 q^{27} - 42 q^{29} - 196 q^{30} - 98 q^{31} - 238 q^{32} - 224 q^{33} - 224 q^{34} - 210 q^{35} - 686 q^{36} - 140 q^{37} - 294 q^{38} - 322 q^{39} - 266 q^{40} - 14 q^{41} - 14 q^{42} - 14 q^{43} + 168 q^{44} + 406 q^{45} + 756 q^{46} + 266 q^{47} + 994 q^{48} + 434 q^{49} + 672 q^{50} + 322 q^{51} + 546 q^{52} + 238 q^{53} + 364 q^{54} + 210 q^{55} + 140 q^{56} - 182 q^{58} - 84 q^{59} - 574 q^{60} - 238 q^{61} - 504 q^{62} - 686 q^{63} - 896 q^{64} - 518 q^{65} - 1022 q^{66} - 574 q^{67} - 1092 q^{68} - 686 q^{69} - 1022 q^{70} + 224 q^{71} + 112 q^{72} - 210 q^{73} + 756 q^{74} + 756 q^{75} + 1106 q^{76} + 616 q^{77} + 882 q^{78} + 182 q^{79} + 1162 q^{80} + 546 q^{81} + 210 q^{82} + 154 q^{83} + 448 q^{84} + 70 q^{85} - 84 q^{87} - 364 q^{88} - 224 q^{89} - 700 q^{90} - 434 q^{91} - 1022 q^{92} - 406 q^{93} - 462 q^{94} - 1022 q^{95} - 1176 q^{96} + 560 q^{97} - 168 q^{98} + 868 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(29))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
29.3.c \(\chi_{29}(12, \cdot)\) 29.3.c.a 8 2
29.3.f \(\chi_{29}(2, \cdot)\) 29.3.f.a 48 12