Properties

Label 128.2
Level 128
Weight 2
Dimension 264
Nonzero newspaces 5
Newforms 11
Sturm bound 2048
Trace bound 9

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Defining parameters

Level: \( N \) = \( 128 = 2^{7} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 5 \)
Newforms: \( 11 \)
Sturm bound: \(2048\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(128))\).

Total New Old
Modular forms 592 312 280
Cusp forms 433 264 169
Eisenstein series 159 48 111

Trace form

\(264q \) \(\mathstrut -\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 12q^{3} \) \(\mathstrut -\mathstrut 16q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 12q^{7} \) \(\mathstrut -\mathstrut 16q^{8} \) \(\mathstrut -\mathstrut 20q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(264q \) \(\mathstrut -\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 12q^{3} \) \(\mathstrut -\mathstrut 16q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 12q^{7} \) \(\mathstrut -\mathstrut 16q^{8} \) \(\mathstrut -\mathstrut 20q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 16q^{12} \) \(\mathstrut -\mathstrut 16q^{13} \) \(\mathstrut -\mathstrut 16q^{14} \) \(\mathstrut -\mathstrut 16q^{15} \) \(\mathstrut -\mathstrut 16q^{16} \) \(\mathstrut -\mathstrut 24q^{17} \) \(\mathstrut -\mathstrut 16q^{18} \) \(\mathstrut -\mathstrut 12q^{19} \) \(\mathstrut -\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut -\mathstrut 16q^{22} \) \(\mathstrut -\mathstrut 20q^{23} \) \(\mathstrut -\mathstrut 16q^{24} \) \(\mathstrut -\mathstrut 36q^{25} \) \(\mathstrut -\mathstrut 16q^{26} \) \(\mathstrut -\mathstrut 36q^{27} \) \(\mathstrut -\mathstrut 16q^{28} \) \(\mathstrut -\mathstrut 32q^{29} \) \(\mathstrut -\mathstrut 16q^{30} \) \(\mathstrut -\mathstrut 32q^{31} \) \(\mathstrut -\mathstrut 16q^{32} \) \(\mathstrut -\mathstrut 64q^{33} \) \(\mathstrut -\mathstrut 16q^{34} \) \(\mathstrut -\mathstrut 36q^{35} \) \(\mathstrut -\mathstrut 16q^{36} \) \(\mathstrut -\mathstrut 32q^{37} \) \(\mathstrut -\mathstrut 16q^{38} \) \(\mathstrut -\mathstrut 36q^{39} \) \(\mathstrut -\mathstrut 16q^{40} \) \(\mathstrut -\mathstrut 36q^{41} \) \(\mathstrut -\mathstrut 16q^{42} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 16q^{44} \) \(\mathstrut -\mathstrut 12q^{45} \) \(\mathstrut -\mathstrut 16q^{46} \) \(\mathstrut -\mathstrut 16q^{47} \) \(\mathstrut -\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut 4q^{49} \) \(\mathstrut +\mathstrut 32q^{50} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut +\mathstrut 80q^{52} \) \(\mathstrut +\mathstrut 16q^{53} \) \(\mathstrut +\mathstrut 112q^{54} \) \(\mathstrut +\mathstrut 20q^{55} \) \(\mathstrut +\mathstrut 96q^{56} \) \(\mathstrut +\mathstrut 44q^{57} \) \(\mathstrut +\mathstrut 128q^{58} \) \(\mathstrut +\mathstrut 20q^{59} \) \(\mathstrut +\mathstrut 176q^{60} \) \(\mathstrut +\mathstrut 48q^{61} \) \(\mathstrut +\mathstrut 80q^{62} \) \(\mathstrut +\mathstrut 48q^{63} \) \(\mathstrut +\mathstrut 176q^{64} \) \(\mathstrut +\mathstrut 48q^{65} \) \(\mathstrut +\mathstrut 176q^{66} \) \(\mathstrut +\mathstrut 28q^{67} \) \(\mathstrut +\mathstrut 80q^{68} \) \(\mathstrut +\mathstrut 36q^{69} \) \(\mathstrut +\mathstrut 176q^{70} \) \(\mathstrut +\mathstrut 20q^{71} \) \(\mathstrut +\mathstrut 128q^{72} \) \(\mathstrut +\mathstrut 44q^{73} \) \(\mathstrut +\mathstrut 96q^{74} \) \(\mathstrut +\mathstrut 112q^{76} \) \(\mathstrut -\mathstrut 12q^{77} \) \(\mathstrut +\mathstrut 80q^{78} \) \(\mathstrut -\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 32q^{80} \) \(\mathstrut -\mathstrut 20q^{81} \) \(\mathstrut -\mathstrut 16q^{82} \) \(\mathstrut -\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 16q^{84} \) \(\mathstrut -\mathstrut 8q^{85} \) \(\mathstrut -\mathstrut 16q^{86} \) \(\mathstrut -\mathstrut 68q^{87} \) \(\mathstrut -\mathstrut 16q^{88} \) \(\mathstrut -\mathstrut 84q^{89} \) \(\mathstrut -\mathstrut 16q^{90} \) \(\mathstrut -\mathstrut 60q^{91} \) \(\mathstrut -\mathstrut 16q^{92} \) \(\mathstrut -\mathstrut 64q^{93} \) \(\mathstrut -\mathstrut 16q^{94} \) \(\mathstrut -\mathstrut 72q^{95} \) \(\mathstrut -\mathstrut 16q^{96} \) \(\mathstrut -\mathstrut 96q^{97} \) \(\mathstrut -\mathstrut 16q^{98} \) \(\mathstrut -\mathstrut 64q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)

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
128.2.a \(\chi_{128}(1, \cdot)\) 128.2.a.a 1 1
128.2.a.b 1
128.2.a.c 1
128.2.a.d 1
128.2.b \(\chi_{128}(65, \cdot)\) 128.2.b.a 2 1
128.2.b.b 2
128.2.e \(\chi_{128}(33, \cdot)\) 128.2.e.a 2 2
128.2.e.b 2
128.2.g \(\chi_{128}(17, \cdot)\) 128.2.g.a 4 4
128.2.g.b 8
128.2.i \(\chi_{128}(9, \cdot)\) None 0 8
128.2.k \(\chi_{128}(5, \cdot)\) 128.2.k.a 240 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(128))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(128)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)