Properties

Label 150.2
Level 150
Weight 2
Dimension 137
Nonzero newspaces 6
Newforms 12
Sturm bound 2400
Trace bound 1

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Defining parameters

Level: \( N \) = \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newforms: \( 12 \)
Sturm bound: \(2400\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(150))\).

Total New Old
Modular forms 712 137 575
Cusp forms 489 137 352
Eisenstein series 223 0 223

Trace form

\(137q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 3q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 7q^{6} \) \(\mathstrut +\mathstrut 24q^{7} \) \(\mathstrut +\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(137q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 3q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 7q^{6} \) \(\mathstrut +\mathstrut 24q^{7} \) \(\mathstrut +\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 9q^{12} \) \(\mathstrut +\mathstrut 10q^{13} \) \(\mathstrut -\mathstrut 8q^{14} \) \(\mathstrut -\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 3q^{16} \) \(\mathstrut -\mathstrut 34q^{17} \) \(\mathstrut -\mathstrut 23q^{18} \) \(\mathstrut -\mathstrut 52q^{19} \) \(\mathstrut -\mathstrut 8q^{20} \) \(\mathstrut -\mathstrut 32q^{21} \) \(\mathstrut -\mathstrut 60q^{22} \) \(\mathstrut -\mathstrut 56q^{23} \) \(\mathstrut -\mathstrut 13q^{24} \) \(\mathstrut -\mathstrut 86q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut +\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 16q^{28} \) \(\mathstrut -\mathstrut 38q^{29} \) \(\mathstrut -\mathstrut 20q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 7q^{32} \) \(\mathstrut -\mathstrut 20q^{33} \) \(\mathstrut -\mathstrut 28q^{34} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 3q^{36} \) \(\mathstrut -\mathstrut 24q^{37} \) \(\mathstrut +\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut 54q^{39} \) \(\mathstrut -\mathstrut 6q^{40} \) \(\mathstrut +\mathstrut 6q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut -\mathstrut 76q^{43} \) \(\mathstrut +\mathstrut 20q^{44} \) \(\mathstrut -\mathstrut 70q^{45} \) \(\mathstrut -\mathstrut 24q^{46} \) \(\mathstrut -\mathstrut 32q^{47} \) \(\mathstrut -\mathstrut 9q^{48} \) \(\mathstrut -\mathstrut 63q^{49} \) \(\mathstrut +\mathstrut 18q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut +\mathstrut 10q^{52} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut +\mathstrut 7q^{54} \) \(\mathstrut -\mathstrut 24q^{55} \) \(\mathstrut +\mathstrut 8q^{56} \) \(\mathstrut -\mathstrut 20q^{57} \) \(\mathstrut +\mathstrut 58q^{58} \) \(\mathstrut +\mathstrut 20q^{59} \) \(\mathstrut +\mathstrut 32q^{60} \) \(\mathstrut +\mathstrut 82q^{61} \) \(\mathstrut +\mathstrut 48q^{62} \) \(\mathstrut +\mathstrut 84q^{63} \) \(\mathstrut +\mathstrut 3q^{64} \) \(\mathstrut +\mathstrut 74q^{65} \) \(\mathstrut +\mathstrut 48q^{66} \) \(\mathstrut +\mathstrut 108q^{67} \) \(\mathstrut +\mathstrut 6q^{68} \) \(\mathstrut +\mathstrut 180q^{69} \) \(\mathstrut +\mathstrut 48q^{70} \) \(\mathstrut +\mathstrut 24q^{71} \) \(\mathstrut +\mathstrut 19q^{72} \) \(\mathstrut +\mathstrut 110q^{73} \) \(\mathstrut +\mathstrut 34q^{74} \) \(\mathstrut +\mathstrut 164q^{75} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut +\mathstrut 96q^{77} \) \(\mathstrut +\mathstrut 118q^{78} \) \(\mathstrut +\mathstrut 64q^{79} \) \(\mathstrut +\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 19q^{81} \) \(\mathstrut +\mathstrut 62q^{82} \) \(\mathstrut +\mathstrut 20q^{83} \) \(\mathstrut +\mathstrut 68q^{84} \) \(\mathstrut +\mathstrut 34q^{85} \) \(\mathstrut +\mathstrut 20q^{86} \) \(\mathstrut +\mathstrut 62q^{87} \) \(\mathstrut +\mathstrut 20q^{88} \) \(\mathstrut +\mathstrut 4q^{89} \) \(\mathstrut +\mathstrut 54q^{90} \) \(\mathstrut +\mathstrut 24q^{92} \) \(\mathstrut -\mathstrut 20q^{93} \) \(\mathstrut +\mathstrut 80q^{94} \) \(\mathstrut +\mathstrut 16q^{95} \) \(\mathstrut -\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 30q^{97} \) \(\mathstrut +\mathstrut 75q^{98} \) \(\mathstrut +\mathstrut 20q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)

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
150.2.a \(\chi_{150}(1, \cdot)\) 150.2.a.a 1 1
150.2.a.b 1
150.2.a.c 1
150.2.c \(\chi_{150}(49, \cdot)\) 150.2.c.a 2 1
150.2.e \(\chi_{150}(107, \cdot)\) 150.2.e.a 4 2
150.2.e.b 8
150.2.g \(\chi_{150}(31, \cdot)\) 150.2.g.a 4 4
150.2.g.b 4
150.2.g.c 8
150.2.h \(\chi_{150}(19, \cdot)\) 150.2.h.a 8 4
150.2.h.b 16
150.2.l \(\chi_{150}(17, \cdot)\) 150.2.l.a 80 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(150))\) into lower level spaces

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