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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

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

Display 100 coefficients 10 coefficients

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 available 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