Properties

Label 29.4
Level 29
Weight 4
Dimension 91
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 280
Trace bound 1

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Defining parameters

Level: \( N \) = \( 29 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(280\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(29))\).

Total New Old
Modular forms 119 117 2
Cusp forms 91 91 0
Eisenstein series 28 26 2

Trace form

\( 91q - 14q^{2} - 14q^{3} - 14q^{4} - 14q^{5} - 14q^{6} - 14q^{7} - 14q^{8} - 14q^{9} + O(q^{10}) \) \( 91q - 14q^{2} - 14q^{3} - 14q^{4} - 14q^{5} - 14q^{6} - 14q^{7} - 14q^{8} - 14q^{9} - 14q^{10} - 14q^{11} - 14q^{12} - 14q^{13} - 14q^{14} - 14q^{15} - 14q^{16} - 14q^{17} - 14q^{18} - 14q^{19} - 938q^{20} - 798q^{21} - 406q^{22} - 42q^{23} + 658q^{24} + 434q^{25} + 756q^{26} + 1078q^{27} + 1540q^{28} + 770q^{29} + 2156q^{30} + 602q^{31} + 882q^{32} + 322q^{33} - 84q^{34} - 406q^{35} - 2366q^{36} - 630q^{37} - 1750q^{38} - 2310q^{39} - 2198q^{40} - 14q^{41} - 14q^{42} - 14q^{43} - 1764q^{44} - 3479q^{45} - 5264q^{46} - 1498q^{47} - 3710q^{48} - 854q^{49} + 84q^{50} + 826q^{51} + 3010q^{52} + 2317q^{53} + 5656q^{54} + 5698q^{55} + 5264q^{56} + 3164q^{57} + 9562q^{58} + 1512q^{59} + 8442q^{60} + 2506q^{61} + 3612q^{62} + 3010q^{63} + 1876q^{64} + 49q^{65} - 1694q^{66} - 1862q^{67} - 5208q^{68} - 4214q^{69} - 16310q^{70} - 9982q^{71} - 21140q^{72} - 9107q^{73} - 8904q^{74} - 3234q^{75} - 2702q^{76} - 294q^{77} + 1554q^{78} + 826q^{79} + 8610q^{80} + 6258q^{81} + 3682q^{82} + 4130q^{83} + 13048q^{84} + 7042q^{85} + 12012q^{86} + 6006q^{87} + 14084q^{88} + 5586q^{89} + 9968q^{90} + 5530q^{91} + 9394q^{92} + 2450q^{93} + 1666q^{94} + 1554q^{95} - 11928q^{96} - 11809q^{97} - 18536q^{98} - 22498q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(29))\)

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
29.4.a \(\chi_{29}(1, \cdot)\) 29.4.a.a 2 1
29.4.a.b 5
29.4.b \(\chi_{29}(28, \cdot)\) 29.4.b.a 6 1
29.4.d \(\chi_{29}(7, \cdot)\) 29.4.d.a 42 6
29.4.e \(\chi_{29}(4, \cdot)\) 29.4.e.a 36 6