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Properties

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

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Defining parameters

Level: \( N \) = \( 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 4 \)
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

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

Display 100 coefficients 10 coefficients

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 available 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