Properties

Label 45.2
Level 45
Weight 2
Dimension 39
Nonzero newspaces 6
Newforms 7
Sturm bound 288
Trace bound 2

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Defining parameters

Level: \( N \) = \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newforms: \( 7 \)
Sturm bound: \(288\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(45))\).

Total New Old
Modular forms 104 65 39
Cusp forms 41 39 2
Eisenstein series 63 26 37

Trace form

\(39q \) \(\mathstrut -\mathstrut 7q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut 11q^{4} \) \(\mathstrut -\mathstrut 9q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 12q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(39q \) \(\mathstrut -\mathstrut 7q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut 11q^{4} \) \(\mathstrut -\mathstrut 9q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 12q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut -\mathstrut 15q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 8q^{12} \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut -\mathstrut 7q^{16} \) \(\mathstrut +\mathstrut 2q^{17} \) \(\mathstrut +\mathstrut 16q^{18} \) \(\mathstrut -\mathstrut 20q^{19} \) \(\mathstrut +\mathstrut 25q^{20} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 12q^{23} \) \(\mathstrut +\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 3q^{25} \) \(\mathstrut +\mathstrut 14q^{26} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut +\mathstrut 8q^{28} \) \(\mathstrut +\mathstrut 22q^{29} \) \(\mathstrut +\mathstrut 32q^{30} \) \(\mathstrut -\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 13q^{32} \) \(\mathstrut +\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 14q^{34} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut -\mathstrut 32q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 16q^{38} \) \(\mathstrut -\mathstrut 32q^{39} \) \(\mathstrut -\mathstrut 23q^{40} \) \(\mathstrut -\mathstrut 50q^{41} \) \(\mathstrut -\mathstrut 36q^{42} \) \(\mathstrut -\mathstrut 32q^{43} \) \(\mathstrut -\mathstrut 68q^{44} \) \(\mathstrut -\mathstrut 28q^{45} \) \(\mathstrut -\mathstrut 40q^{46} \) \(\mathstrut -\mathstrut 40q^{47} \) \(\mathstrut -\mathstrut 40q^{48} \) \(\mathstrut +\mathstrut 3q^{49} \) \(\mathstrut -\mathstrut 31q^{50} \) \(\mathstrut -\mathstrut 16q^{51} \) \(\mathstrut +\mathstrut 2q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 4q^{54} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut +\mathstrut 16q^{57} \) \(\mathstrut +\mathstrut 26q^{58} \) \(\mathstrut +\mathstrut 44q^{59} \) \(\mathstrut +\mathstrut 20q^{60} \) \(\mathstrut +\mathstrut 26q^{61} \) \(\mathstrut +\mathstrut 84q^{62} \) \(\mathstrut +\mathstrut 60q^{63} \) \(\mathstrut +\mathstrut 49q^{64} \) \(\mathstrut +\mathstrut 62q^{65} \) \(\mathstrut +\mathstrut 88q^{66} \) \(\mathstrut +\mathstrut 24q^{67} \) \(\mathstrut +\mathstrut 70q^{68} \) \(\mathstrut +\mathstrut 60q^{69} \) \(\mathstrut +\mathstrut 60q^{70} \) \(\mathstrut +\mathstrut 64q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut -\mathstrut 2q^{73} \) \(\mathstrut -\mathstrut 2q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut +\mathstrut 36q^{76} \) \(\mathstrut -\mathstrut 12q^{77} \) \(\mathstrut -\mathstrut 40q^{78} \) \(\mathstrut -\mathstrut 12q^{79} \) \(\mathstrut -\mathstrut 35q^{80} \) \(\mathstrut -\mathstrut 40q^{81} \) \(\mathstrut -\mathstrut 30q^{82} \) \(\mathstrut -\mathstrut 72q^{83} \) \(\mathstrut -\mathstrut 72q^{84} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut -\mathstrut 100q^{86} \) \(\mathstrut -\mathstrut 44q^{87} \) \(\mathstrut -\mathstrut 66q^{89} \) \(\mathstrut -\mathstrut 104q^{90} \) \(\mathstrut -\mathstrut 48q^{91} \) \(\mathstrut -\mathstrut 96q^{92} \) \(\mathstrut -\mathstrut 60q^{93} \) \(\mathstrut -\mathstrut 4q^{94} \) \(\mathstrut -\mathstrut 40q^{95} \) \(\mathstrut -\mathstrut 56q^{96} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 83q^{98} \) \(\mathstrut -\mathstrut 20q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)

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
45.2.a \(\chi_{45}(1, \cdot)\) 45.2.a.a 1 1
45.2.b \(\chi_{45}(19, \cdot)\) 45.2.b.a 2 1
45.2.e \(\chi_{45}(16, \cdot)\) 45.2.e.a 2 2
45.2.e.b 6
45.2.f \(\chi_{45}(8, \cdot)\) 45.2.f.a 4 2
45.2.j \(\chi_{45}(4, \cdot)\) 45.2.j.a 8 2
45.2.l \(\chi_{45}(2, \cdot)\) 45.2.l.a 16 4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(45))\) into lower level spaces

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