Properties

Label 128.3
Level 128
Weight 3
Dimension 552
Nonzero newspaces 5
Newform subspaces 9
Sturm bound 3072
Trace bound 9

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Defining parameters

Level: \( N \) = \( 128 = 2^{7} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 9 \)
Sturm bound: \(3072\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(128))\).

Total New Old
Modular forms 1104 600 504
Cusp forms 944 552 392
Eisenstein series 160 48 112

Trace form

\( 552q - 16q^{2} - 12q^{3} - 16q^{4} - 16q^{5} - 16q^{6} - 12q^{7} - 16q^{8} - 20q^{9} + O(q^{10}) \) \( 552q - 16q^{2} - 12q^{3} - 16q^{4} - 16q^{5} - 16q^{6} - 12q^{7} - 16q^{8} - 20q^{9} - 16q^{10} - 12q^{11} - 16q^{12} - 16q^{13} - 16q^{14} - 8q^{15} - 16q^{16} - 24q^{17} - 16q^{18} - 12q^{19} - 16q^{20} + 20q^{21} - 16q^{22} + 52q^{23} - 16q^{24} + 76q^{25} - 16q^{26} + 84q^{27} - 16q^{28} + 16q^{29} - 16q^{30} - 16q^{31} - 16q^{32} - 96q^{33} - 16q^{34} - 108q^{35} - 16q^{36} - 112q^{37} - 16q^{38} - 204q^{39} - 16q^{40} - 180q^{41} - 16q^{42} - 108q^{43} - 16q^{44} - 188q^{45} - 16q^{46} - 8q^{47} - 16q^{48} - 220q^{49} - 640q^{50} - 240q^{51} - 1072q^{52} - 336q^{53} - 1168q^{54} - 268q^{55} - 800q^{56} - 404q^{57} - 736q^{58} - 140q^{59} - 592q^{60} - 144q^{61} - 112q^{62} - 32q^{63} + 176q^{64} + 112q^{65} + 560q^{66} + 148q^{67} + 464q^{68} + 404q^{69} + 1328q^{70} + 244q^{71} + 1280q^{72} + 620q^{73} + 1216q^{74} + 472q^{75} + 1648q^{76} + 628q^{77} + 1424q^{78} + 504q^{79} + 800q^{80} + 748q^{81} - 16q^{82} + 468q^{83} - 16q^{84} + 504q^{85} - 16q^{86} + 436q^{87} - 16q^{88} + 364q^{89} - 16q^{90} + 180q^{91} - 16q^{92} + 80q^{93} - 16q^{94} - 16q^{95} - 16q^{96} - 160q^{97} - 16q^{98} - 232q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(128))\)

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
128.3.c \(\chi_{128}(127, \cdot)\) 128.3.c.a 4 1
128.3.c.b 4
128.3.d \(\chi_{128}(63, \cdot)\) 128.3.d.a 2 1
128.3.d.b 2
128.3.d.c 4
128.3.f \(\chi_{128}(31, \cdot)\) 128.3.f.a 6 2
128.3.f.b 6
128.3.h \(\chi_{128}(15, \cdot)\) 128.3.h.a 28 4
128.3.j \(\chi_{128}(7, \cdot)\) None 0 8
128.3.l \(\chi_{128}(3, \cdot)\) 128.3.l.a 496 16

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(128))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(128)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)