Properties

Label 150.3
Level 150
Weight 3
Dimension 276
Nonzero newspaces 6
Newform subspaces 13
Sturm bound 3600
Trace bound 3

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Defining parameters

Level: \( N \) = \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 13 \)
Sturm bound: \(3600\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(150))\).

Total New Old
Modular forms 1312 276 1036
Cusp forms 1088 276 812
Eisenstein series 224 0 224

Trace form

\( 276q - 8q^{2} - 8q^{3} + 16q^{6} + 16q^{7} + 16q^{8} + 80q^{9} + O(q^{10}) \) \( 276q - 8q^{2} - 8q^{3} + 16q^{6} + 16q^{7} + 16q^{8} + 80q^{9} + 12q^{10} + 32q^{11} + 16q^{12} + 56q^{13} - 4q^{15} - 32q^{16} + 192q^{17} - 28q^{18} + 240q^{19} + 32q^{20} - 8q^{21} + 96q^{22} + 112q^{23} - 156q^{25} - 128q^{26} - 56q^{27} - 192q^{28} - 400q^{29} - 240q^{30} - 208q^{31} - 48q^{32} - 312q^{33} - 180q^{34} - 328q^{35} + 48q^{36} + 512q^{37} + 128q^{38} + 480q^{39} + 24q^{40} + 256q^{41} + 160q^{42} + 272q^{43} + 380q^{45} - 160q^{46} - 32q^{47} - 32q^{48} - 480q^{49} - 92q^{50} - 424q^{51} - 208q^{52} - 560q^{53} - 480q^{54} - 944q^{55} - 128q^{56} - 1040q^{57} - 128q^{58} - 800q^{59} - 208q^{60} - 32q^{61} + 160q^{62} - 1052q^{63} + 44q^{65} + 160q^{66} + 688q^{67} + 176q^{68} - 300q^{69} + 48q^{70} - 128q^{71} + 80q^{72} - 24q^{73} + 404q^{75} + 192q^{76} + 256q^{77} + 128q^{78} + 800q^{79} + 200q^{81} - 448q^{82} + 256q^{83} + 120q^{84} + 744q^{85} - 192q^{86} + 1396q^{87} + 128q^{88} + 100q^{89} + 924q^{90} + 224q^{91} + 64q^{92} + 748q^{93} + 640q^{94} + 256q^{95} + 64q^{96} - 776q^{97} + 248q^{98} - 160q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(150))\)

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
150.3.b \(\chi_{150}(149, \cdot)\) 150.3.b.a 4 1
150.3.b.b 8
150.3.d \(\chi_{150}(101, \cdot)\) 150.3.d.a 2 1
150.3.d.b 2
150.3.d.c 4
150.3.d.d 4
150.3.f \(\chi_{150}(7, \cdot)\) 150.3.f.a 4 2
150.3.f.b 4
150.3.f.c 4
150.3.i \(\chi_{150}(29, \cdot)\) 150.3.i.a 80 4
150.3.j \(\chi_{150}(11, \cdot)\) 150.3.j.a 80 4
150.3.k \(\chi_{150}(13, \cdot)\) 150.3.k.a 32 8
150.3.k.b 48

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(150))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(150)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)