Properties

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

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Defining parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 2 \)
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

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

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

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