Properties

Label 10.4
Level 10
Weight 4
Dimension 3
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 24
Trace bound 1

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Defining parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(10))\).

Total New Old
Modular forms 13 3 10
Cusp forms 5 3 2
Eisenstein series 8 0 8

Trace form

\( 3 q + 2 q^{2} - 8 q^{3} - 4 q^{4} - 5 q^{5} - 8 q^{6} - 4 q^{7} + 8 q^{8} + 83 q^{9} + O(q^{10}) \) \( 3 q + 2 q^{2} - 8 q^{3} - 4 q^{4} - 5 q^{5} - 8 q^{6} - 4 q^{7} + 8 q^{8} + 83 q^{9} + 50 q^{10} - 44 q^{11} - 32 q^{12} - 58 q^{13} - 112 q^{14} - 80 q^{15} + 48 q^{16} + 66 q^{17} + 74 q^{18} + 20 q^{19} + 60 q^{20} + 136 q^{21} + 24 q^{22} + 132 q^{23} - 96 q^{24} - 125 q^{25} - 68 q^{26} - 80 q^{27} - 16 q^{28} - 270 q^{29} - 120 q^{30} - 104 q^{31} + 32 q^{32} - 96 q^{33} + 388 q^{34} + 500 q^{35} - 36 q^{36} - 34 q^{37} - 200 q^{38} + 416 q^{39} - 120 q^{40} + 46 q^{41} + 64 q^{42} + 32 q^{43} + 272 q^{44} - 45 q^{45} + 32 q^{46} - 204 q^{47} - 128 q^{48} - 993 q^{49} - 350 q^{50} - 784 q^{51} - 232 q^{52} + 222 q^{53} + 240 q^{54} + 340 q^{55} + 384 q^{56} + 800 q^{57} - 180 q^{58} + 460 q^{59} + 1986 q^{61} + 304 q^{62} - 148 q^{63} - 64 q^{64} - 530 q^{65} - 416 q^{66} - 1024 q^{67} + 264 q^{68} - 824 q^{69} + 480 q^{70} - 1824 q^{71} + 296 q^{72} + 362 q^{73} - 1012 q^{74} + 200 q^{75} - 880 q^{76} - 48 q^{77} + 928 q^{78} + 1280 q^{79} - 80 q^{80} + 483 q^{81} - 876 q^{82} + 72 q^{83} - 288 q^{84} - 950 q^{85} + 1512 q^{86} + 720 q^{87} + 96 q^{88} + 1790 q^{89} + 1290 q^{90} + 856 q^{91} + 528 q^{92} - 1216 q^{93} - 1312 q^{94} - 1100 q^{95} - 128 q^{96} + 1106 q^{97} - 654 q^{98} - 844 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)

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
10.4.a \(\chi_{10}(1, \cdot)\) 10.4.a.a 1 1
10.4.b \(\chi_{10}(9, \cdot)\) 10.4.b.a 2 1

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)