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Properties

Label 128.6
Level 128
Weight 6
Dimension 1416
Nonzero newspaces 5
Sturm bound 6144
Trace bound 9

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Defining parameters

Level: \( N \) = \( 128 = 2^{7} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 5 \)
Sturm bound: \(6144\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(128))\).

Total New Old
Modular forms 2640 1464 1176
Cusp forms 2480 1416 1064
Eisenstein series 160 48 112

Trace form

\( 1416 q - 16 q^{2} - 12 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 12 q^{7} - 16 q^{8} - 20 q^{9} + O(q^{10}) \) \( 1416 q - 16 q^{2} - 12 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 12 q^{7} - 16 q^{8} - 20 q^{9} - 16 q^{10} - 12 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 24 q^{17} - 16 q^{18} - 12 q^{19} - 16 q^{20} - 988 q^{21} - 16 q^{22} - 1684 q^{23} - 16 q^{24} + 12444 q^{25} - 16 q^{26} + 7452 q^{27} - 16 q^{28} - 8160 q^{29} - 16 q^{30} - 23072 q^{31} - 16 q^{32} - 22720 q^{33} - 16 q^{34} + 4764 q^{35} - 16 q^{36} + 21280 q^{37} - 16 q^{38} + 44892 q^{39} - 16 q^{40} + 9884 q^{41} - 16 q^{42} - 32084 q^{43} - 16 q^{44} - 10572 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} + 67204 q^{49} + 274112 q^{50} + 19896 q^{51} - 146992 q^{52} - 98928 q^{53} - 466576 q^{54} - 110060 q^{55} - 301856 q^{56} - 103124 q^{57} - 52000 q^{58} + 28948 q^{59} + 395696 q^{60} + 192304 q^{61} + 351248 q^{62} + 158768 q^{63} + 749744 q^{64} + 221488 q^{65} + 509744 q^{66} + 61148 q^{67} + 14288 q^{68} - 90268 q^{69} - 573904 q^{70} - 143852 q^{71} - 828160 q^{72} - 420564 q^{73} - 755456 q^{74} - 205760 q^{75} - 536976 q^{76} - 97036 q^{77} + 389648 q^{78} - 16 q^{79} + 986912 q^{80} + 321004 q^{81} - 16 q^{82} + 329228 q^{83} - 16 q^{84} + 289784 q^{85} - 16 q^{86} + 282172 q^{87} - 16 q^{88} + 25260 q^{89} - 16 q^{90} - 200124 q^{91} - 16 q^{92} - 362368 q^{93} - 16 q^{94} - 577608 q^{95} - 16 q^{96} - 528736 q^{97} - 16 q^{98} - 338560 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(128))\)

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
128.6.a \(\chi_{128}(1, \cdot)\) 128.6.a.a 1 1
128.6.a.b 1
128.6.a.c 1
128.6.a.d 1
128.6.a.e 2
128.6.a.f 2
128.6.a.g 2
128.6.a.h 2
128.6.a.i 2
128.6.a.j 2
128.6.a.k 2
128.6.a.l 2
128.6.b \(\chi_{128}(65, \cdot)\) 128.6.b.a 2 1
128.6.b.b 2
128.6.b.c 4
128.6.b.d 4
128.6.b.e 4
128.6.b.f 4
128.6.e \(\chi_{128}(33, \cdot)\) 128.6.e.a 18 2
128.6.e.b 18
128.6.g \(\chi_{128}(17, \cdot)\) 128.6.g.a 76 4
128.6.i \(\chi_{128}(9, \cdot)\) None 0 8
128.6.k \(\chi_{128}(5, \cdot)\) n/a 1264 16

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(128))\) into lower level spaces

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