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Properties

Label 128.10
Level 128
Weight 10
Dimension 2568
Nonzero newspaces 5
Sturm bound 10240
Trace bound 9

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Defining parameters

Level: \( N \) = \( 128 = 2^{7} \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 5 \)
Sturm bound: \(10240\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(128))\).

Total New Old
Modular forms 4688 2616 2072
Cusp forms 4528 2568 1960
Eisenstein series 160 48 112

Trace form

\( 2568 q - 16 q^{2} - 12 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 12 q^{7} - 16 q^{8} - 20 q^{9} + O(q^{10}) \) \( 2568 q - 16 q^{2} - 12 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 12 q^{7} - 16 q^{8} - 20 q^{9} - 16 q^{10} - 12 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 24 q^{17} - 16 q^{18} - 12 q^{19} - 16 q^{20} - 78748 q^{21} - 16 q^{22} + 3465964 q^{23} - 16 q^{24} - 6887076 q^{25} - 16 q^{26} + 12650076 q^{27} - 16 q^{28} + 1266784 q^{29} - 16 q^{30} - 22164512 q^{31} - 16 q^{32} + 151232 q^{33} - 16 q^{34} + 38240604 q^{35} - 16 q^{36} + 2429536 q^{37} - 16 q^{38} - 72274212 q^{39} - 16 q^{40} + 15123804 q^{41} - 16 q^{42} + 38062444 q^{43} - 16 q^{44} - 7655052 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} + 161414404 q^{49} - 365516608 q^{50} - 180107400 q^{51} + 50454992 q^{52} + 299631376 q^{53} + 1292464496 q^{54} + 140108820 q^{55} - 406326048 q^{56} - 632899028 q^{57} - 1710306592 q^{58} - 288075244 q^{59} - 461878864 q^{60} + 360484400 q^{61} + 1195227152 q^{62} + 630118448 q^{63} + 2729619632 q^{64} + 502448688 q^{65} - 372019408 q^{66} - 503547492 q^{67} - 2008655920 q^{68} - 1529519452 q^{69} - 3738184144 q^{70} - 238101484 q^{71} + 1429458176 q^{72} + 1774799404 q^{73} + 4364366592 q^{74} + 1146770560 q^{75} + 1777421936 q^{76} - 985591308 q^{77} - 6439686640 q^{78} - 16 q^{79} + 1824710432 q^{80} + 1912077292 q^{81} - 16 q^{82} - 2478583732 q^{83} - 16 q^{84} - 842795016 q^{85} - 16 q^{86} + 2350951612 q^{87} - 16 q^{88} + 4124763564 q^{89} - 16 q^{90} + 1091566788 q^{91} - 16 q^{92} - 2143933120 q^{93} - 16 q^{94} - 5212840008 q^{95} - 16 q^{96} - 3471188576 q^{97} - 16 q^{98} + 1556903744 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(128))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
128.10.a \(\chi_{128}(1, \cdot)\) 128.10.a.a 1 1
128.10.a.b 1
128.10.a.c 1
128.10.a.d 1
128.10.a.e 4
128.10.a.f 4
128.10.a.g 4
128.10.a.h 4
128.10.a.i 4
128.10.a.j 4
128.10.a.k 4
128.10.a.l 4
128.10.b \(\chi_{128}(65, \cdot)\) 128.10.b.a 2 1
128.10.b.b 2
128.10.b.c 4
128.10.b.d 4
128.10.b.e 8
128.10.b.f 8
128.10.b.g 8
128.10.e \(\chi_{128}(33, \cdot)\) 128.10.e.a 34 2
128.10.e.b 34
128.10.g \(\chi_{128}(17, \cdot)\) n/a 140 4
128.10.i \(\chi_{128}(9, \cdot)\) None 0 8
128.10.k \(\chi_{128}(5, \cdot)\) n/a 2288 16

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

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(128))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(128)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 7}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 5}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)