Properties

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

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Defining parameters

Level: \( N \) = \( 29 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 2 \)
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

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

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 the 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