Properties

Label 29.2
Level 29
Weight 2
Dimension 22
Nonzero newspaces 4
Newforms 4
Sturm bound 140
Trace bound 2

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Defining parameters

Level: \( N \) = \( 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newforms: \( 4 \)
Sturm bound: \(140\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(29))\).

Total New Old
Modular forms 49 49 0
Cusp forms 22 22 0
Eisenstein series 27 27 0

Trace form

\(22q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut -\mathstrut 7q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut -\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(22q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut -\mathstrut 7q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut -\mathstrut q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut -\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 14q^{12} \) \(\mathstrut +\mathstrut 10q^{14} \) \(\mathstrut +\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 17q^{16} \) \(\mathstrut +\mathstrut 4q^{17} \) \(\mathstrut +\mathstrut 25q^{18} \) \(\mathstrut +\mathstrut 6q^{19} \) \(\mathstrut +\mathstrut 7q^{20} \) \(\mathstrut -\mathstrut 10q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 38q^{24} \) \(\mathstrut -\mathstrut 11q^{25} \) \(\mathstrut -\mathstrut 7q^{26} \) \(\mathstrut -\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 28q^{28} \) \(\mathstrut -\mathstrut 13q^{29} \) \(\mathstrut -\mathstrut 40q^{30} \) \(\mathstrut -\mathstrut 10q^{31} \) \(\mathstrut -\mathstrut 7q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut -\mathstrut 7q^{36} \) \(\mathstrut +\mathstrut 10q^{37} \) \(\mathstrut +\mathstrut 18q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 55q^{40} \) \(\mathstrut +\mathstrut 28q^{41} \) \(\mathstrut +\mathstrut 82q^{42} \) \(\mathstrut +\mathstrut 30q^{43} \) \(\mathstrut +\mathstrut 56q^{44} \) \(\mathstrut +\mathstrut 29q^{45} \) \(\mathstrut -\mathstrut 12q^{46} \) \(\mathstrut +\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 2q^{48} \) \(\mathstrut -\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut 19q^{50} \) \(\mathstrut +\mathstrut 2q^{51} \) \(\mathstrut -\mathstrut 28q^{52} \) \(\mathstrut -\mathstrut 23q^{53} \) \(\mathstrut -\mathstrut 20q^{54} \) \(\mathstrut -\mathstrut 54q^{55} \) \(\mathstrut -\mathstrut 20q^{56} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 95q^{58} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut -\mathstrut 42q^{60} \) \(\mathstrut -\mathstrut 8q^{61} \) \(\mathstrut -\mathstrut 16q^{62} \) \(\mathstrut -\mathstrut 22q^{63} \) \(\mathstrut -\mathstrut 13q^{64} \) \(\mathstrut +\mathstrut 7q^{65} \) \(\mathstrut +\mathstrut 18q^{66} \) \(\mathstrut -\mathstrut 2q^{67} \) \(\mathstrut +\mathstrut 14q^{68} \) \(\mathstrut +\mathstrut 26q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 12q^{71} \) \(\mathstrut +\mathstrut 27q^{72} \) \(\mathstrut -\mathstrut 3q^{73} \) \(\mathstrut +\mathstrut 2q^{74} \) \(\mathstrut +\mathstrut 40q^{75} \) \(\mathstrut +\mathstrut 14q^{76} \) \(\mathstrut +\mathstrut 12q^{77} \) \(\mathstrut +\mathstrut 42q^{78} \) \(\mathstrut +\mathstrut 38q^{79} \) \(\mathstrut -\mathstrut 24q^{80} \) \(\mathstrut -\mathstrut 5q^{81} \) \(\mathstrut +\mathstrut 56q^{82} \) \(\mathstrut +\mathstrut 14q^{83} \) \(\mathstrut +\mathstrut 10q^{85} \) \(\mathstrut -\mathstrut 36q^{86} \) \(\mathstrut +\mathstrut 32q^{87} \) \(\mathstrut -\mathstrut 16q^{88} \) \(\mathstrut +\mathstrut 6q^{89} \) \(\mathstrut +\mathstrut 38q^{90} \) \(\mathstrut +\mathstrut 14q^{91} \) \(\mathstrut -\mathstrut 14q^{92} \) \(\mathstrut +\mathstrut 58q^{93} \) \(\mathstrut +\mathstrut 74q^{94} \) \(\mathstrut -\mathstrut 6q^{95} \) \(\mathstrut +\mathstrut 7q^{97} \) \(\mathstrut -\mathstrut 25q^{98} \) \(\mathstrut -\mathstrut 40q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)

We only show spaces with even 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
29.2.a \(\chi_{29}(1, \cdot)\) 29.2.a.a 2 1
29.2.b \(\chi_{29}(28, \cdot)\) 29.2.b.a 2 1
29.2.d \(\chi_{29}(7, \cdot)\) 29.2.d.a 6 6
29.2.e \(\chi_{29}(4, \cdot)\) 29.2.e.a 12 6