Properties

Label 45.3
Level 45
Weight 3
Dimension 92
Nonzero newspaces 6
Newform subspaces 7
Sturm bound 432
Trace bound 4

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Defining parameters

Level: \( N \) = \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 7 \)
Sturm bound: \(432\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(45))\).

Total New Old
Modular forms 176 120 56
Cusp forms 112 92 20
Eisenstein series 64 28 36

Trace form

\( 92q + 2q^{2} - 2q^{3} - 2q^{4} - 10q^{5} - 34q^{6} - 36q^{8} - 10q^{9} + O(q^{10}) \) \( 92q + 2q^{2} - 2q^{3} - 2q^{4} - 10q^{5} - 34q^{6} - 36q^{8} - 10q^{9} - 68q^{10} - 50q^{11} - 52q^{12} - 28q^{13} - 24q^{14} + 4q^{15} + 34q^{16} + 68q^{17} + 40q^{18} + 20q^{19} + 66q^{20} - 12q^{21} - 106q^{22} - 28q^{23} + 6q^{24} - 94q^{25} - 200q^{26} - 164q^{27} - 120q^{28} - 168q^{29} + 14q^{30} + 120q^{31} + 278q^{32} + 158q^{33} + 290q^{34} + 392q^{35} + 610q^{36} + 208q^{37} + 678q^{38} + 400q^{39} + 222q^{40} + 274q^{41} + 228q^{42} - 142q^{43} - 94q^{45} - 336q^{46} - 280q^{47} - 682q^{48} - 494q^{49} - 1030q^{50} - 658q^{51} - 380q^{52} - 664q^{53} - 586q^{54} + 4q^{55} - 828q^{56} - 350q^{57} + 136q^{58} - 366q^{59} - 478q^{60} - 184q^{61} - 188q^{62} - 108q^{63} + 236q^{64} + 188q^{65} + 28q^{66} + 222q^{67} + 442q^{68} + 252q^{69} + 408q^{70} + 520q^{71} + 642q^{72} + 236q^{73} + 1044q^{74} + 1066q^{75} + 22q^{76} + 952q^{77} + 1352q^{78} - 168q^{79} + 1280q^{80} + 938q^{81} + 76q^{82} + 908q^{83} + 1164q^{84} + 178q^{85} + 1438q^{86} + 640q^{87} + 30q^{88} - 278q^{90} + 192q^{91} - 1048q^{92} - 972q^{93} - 412q^{94} - 1086q^{95} - 1184q^{96} - 122q^{97} - 1688q^{98} - 1292q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(45))\)

We only show spaces with odd 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
45.3.c \(\chi_{45}(26, \cdot)\) 45.3.c.a 4 1
45.3.d \(\chi_{45}(44, \cdot)\) 45.3.d.a 4 1
45.3.g \(\chi_{45}(28, \cdot)\) 45.3.g.a 4 2
45.3.g.b 4
45.3.h \(\chi_{45}(14, \cdot)\) 45.3.h.a 20 2
45.3.i \(\chi_{45}(11, \cdot)\) 45.3.i.a 16 2
45.3.k \(\chi_{45}(7, \cdot)\) 45.3.k.a 40 4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(45))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(45)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)