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Properties

Label 128.7
Level 128
Weight 7
Dimension 1704
Nonzero newspaces 5
Sturm bound 7168
Trace bound 9

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Defining parameters

Level: \( N \) = \( 128 = 2^{7} \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 5 \)
Sturm bound: \(7168\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(128))\).

Total New Old
Modular forms 3152 1752 1400
Cusp forms 2992 1704 1288
Eisenstein series 160 48 112

Trace form

\( 1704 q - 16 q^{2} - 12 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 12 q^{7} - 16 q^{8} - 20 q^{9} + O(q^{10}) \) \( 1704 q - 16 q^{2} - 12 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 12 q^{7} - 16 q^{8} - 20 q^{9} - 16 q^{10} - 12 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 8 q^{15} - 16 q^{16} - 24 q^{17} - 16 q^{18} - 12 q^{19} - 16 q^{20} + 2900 q^{21} - 16 q^{22} - 13132 q^{23} - 16 q^{24} - 41204 q^{25} - 16 q^{26} + 68628 q^{27} - 16 q^{28} + 66384 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 176352 q^{33} - 16 q^{34} - 162348 q^{35} - 16 q^{36} - 7216 q^{37} - 16 q^{38} + 254388 q^{39} - 16 q^{40} + 217100 q^{41} - 16 q^{42} - 145452 q^{43} - 16 q^{44} - 68348 q^{45} - 16 q^{46} - 8 q^{47} - 16 q^{48} - 470620 q^{49} - 1410880 q^{50} + 157776 q^{51} + 2550224 q^{52} + 887344 q^{53} + 2519408 q^{54} + 232692 q^{55} - 653088 q^{56} - 1088660 q^{57} - 3540256 q^{58} - 886156 q^{59} - 5023312 q^{60} - 1306000 q^{61} - 1083376 q^{62} - 32 q^{63} + 2310320 q^{64} + 1491312 q^{65} + 6205232 q^{66} + 1509588 q^{67} + 3694544 q^{68} + 2169812 q^{69} + 4544048 q^{70} + 266996 q^{71} - 1574656 q^{72} - 2056340 q^{73} - 5848320 q^{74} - 2083688 q^{75} - 9130384 q^{76} - 1395340 q^{77} - 1905136 q^{78} + 1721848 q^{79} + 8356640 q^{80} - 295700 q^{81} - 16 q^{82} - 3074412 q^{83} - 16 q^{84} - 619016 q^{85} - 16 q^{86} + 2029876 q^{87} - 16 q^{88} + 4701292 q^{89} - 16 q^{90} + 3700788 q^{91} - 16 q^{92} + 2349584 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 3416480 q^{97} - 16 q^{98} - 5967784 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(128))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
128.7.c \(\chi_{128}(127, \cdot)\) 128.7.c.a 12 1
128.7.c.b 12
128.7.d \(\chi_{128}(63, \cdot)\) 128.7.d.a 2 1
128.7.d.b 2
128.7.d.c 2
128.7.d.d 2
128.7.d.e 4
128.7.d.f 12
128.7.f \(\chi_{128}(31, \cdot)\) 128.7.f.a 22 2
128.7.f.b 22
128.7.h \(\chi_{128}(15, \cdot)\) 128.7.h.a 92 4
128.7.j \(\chi_{128}(7, \cdot)\) None 0 8
128.7.l \(\chi_{128}(3, \cdot)\) n/a 1520 16

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(128))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(128)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)