↑

Properties

Label 928.2
Level 928
Weight 2
Dimension 14814
Nonzero newspaces 20
Newform subspaces 50
Sturm bound 107520
Trace bound 9

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 928 = 2^{5} \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Newform subspaces: \( 50 \)
Sturm bound: \(107520\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(928))\).

Total New Old
Modular forms 27776 15354 12422
Cusp forms 25985 14814 11171
Eisenstein series 1791 540 1251

Trace form

\( 14814 q - 104 q^{2} - 76 q^{3} - 104 q^{4} - 100 q^{5} - 104 q^{6} - 76 q^{7} - 104 q^{8} - 154 q^{9} + O(q^{10}) \) \( 14814 q - 104 q^{2} - 76 q^{3} - 104 q^{4} - 100 q^{5} - 104 q^{6} - 76 q^{7} - 104 q^{8} - 154 q^{9} - 120 q^{10} - 76 q^{11} - 136 q^{12} - 116 q^{13} - 136 q^{14} - 84 q^{15} - 144 q^{16} - 60 q^{17} - 144 q^{18} - 76 q^{19} - 136 q^{20} - 104 q^{21} - 128 q^{22} - 92 q^{23} - 80 q^{24} - 158 q^{25} - 64 q^{26} - 124 q^{27} - 64 q^{28} - 98 q^{29} - 152 q^{30} - 116 q^{31} - 64 q^{32} - 264 q^{33} - 80 q^{34} - 124 q^{35} - 48 q^{36} - 100 q^{37} - 120 q^{38} - 124 q^{39} - 128 q^{40} - 180 q^{41} - 144 q^{42} - 92 q^{43} - 184 q^{44} - 140 q^{45} - 168 q^{46} - 84 q^{47} - 208 q^{48} - 42 q^{49} - 184 q^{50} - 68 q^{51} - 120 q^{52} - 164 q^{53} - 128 q^{54} - 12 q^{55} - 128 q^{56} - 160 q^{57} - 104 q^{58} - 96 q^{59} - 96 q^{60} - 148 q^{61} - 64 q^{62} + 12 q^{63} - 32 q^{64} - 240 q^{65} - 56 q^{66} + 4 q^{67} - 144 q^{68} - 168 q^{69} - 80 q^{70} - 12 q^{71} - 152 q^{72} - 148 q^{73} - 136 q^{74} - 52 q^{75} - 104 q^{76} - 136 q^{77} - 184 q^{78} - 84 q^{79} - 96 q^{80} - 74 q^{81} - 104 q^{82} - 156 q^{83} - 144 q^{84} - 136 q^{85} - 64 q^{86} - 136 q^{87} - 224 q^{88} - 180 q^{89} - 128 q^{90} - 172 q^{91} - 32 q^{92} - 80 q^{93} - 128 q^{94} - 196 q^{95} - 112 q^{96} - 300 q^{97} - 64 q^{98} - 180 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(928))\)

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
928.2.a \(\chi_{928}(1, \cdot)\) 928.2.a.a 1 1
928.2.a.b 1
928.2.a.c 2
928.2.a.d 2
928.2.a.e 2
928.2.a.f 4
928.2.a.g 5
928.2.a.h 5
928.2.a.i 6
928.2.c \(\chi_{928}(465, \cdot)\) 928.2.c.a 28 1
928.2.e \(\chi_{928}(289, \cdot)\) 928.2.e.a 2 1
928.2.e.b 4
928.2.e.c 12
928.2.e.d 12
928.2.g \(\chi_{928}(753, \cdot)\) 928.2.g.a 4 1
928.2.g.b 24
928.2.j \(\chi_{928}(679, \cdot)\) None 0 2
928.2.k \(\chi_{928}(191, \cdot)\) 928.2.k.a 2 2
928.2.k.b 2
928.2.k.c 4
928.2.k.d 4
928.2.k.e 10
928.2.k.f 10
928.2.k.g 14
928.2.k.h 14
928.2.m \(\chi_{928}(57, \cdot)\) None 0 2
928.2.n \(\chi_{928}(233, \cdot)\) None 0 2
928.2.q \(\chi_{928}(655, \cdot)\) 928.2.q.a 56 2
928.2.t \(\chi_{928}(215, \cdot)\) None 0 2
928.2.u \(\chi_{928}(65, \cdot)\) 928.2.u.a 6 6
928.2.u.b 6
928.2.u.c 12
928.2.u.d 36
928.2.u.e 36
928.2.u.f 36
928.2.u.g 48
928.2.v \(\chi_{928}(117, \cdot)\) 928.2.v.a 448 4
928.2.x \(\chi_{928}(307, \cdot)\) 928.2.x.a 472 4
928.2.ba \(\chi_{928}(75, \cdot)\) 928.2.ba.a 472 4
928.2.bc \(\chi_{928}(173, \cdot)\) 928.2.bc.a 472 4
928.2.be \(\chi_{928}(209, \cdot)\) 928.2.be.a 168 6
928.2.bg \(\chi_{928}(33, \cdot)\) 928.2.bg.a 12 6
928.2.bg.b 72
928.2.bg.c 96
928.2.bi \(\chi_{928}(49, \cdot)\) 928.2.bi.a 168 6
928.2.bk \(\chi_{928}(55, \cdot)\) None 0 12
928.2.bn \(\chi_{928}(15, \cdot)\) 928.2.bn.a 336 12
928.2.bq \(\chi_{928}(25, \cdot)\) None 0 12
928.2.br \(\chi_{928}(9, \cdot)\) None 0 12
928.2.bt \(\chi_{928}(31, \cdot)\) 928.2.bt.a 84 12
928.2.bt.b 84
928.2.bt.c 96
928.2.bt.d 96
928.2.bu \(\chi_{928}(39, \cdot)\) None 0 12
928.2.bx \(\chi_{928}(5, \cdot)\) 928.2.bx.a 2832 24
928.2.bz \(\chi_{928}(11, \cdot)\) 928.2.bz.a 2832 24
928.2.ca \(\chi_{928}(3, \cdot)\) 928.2.ca.a 2832 24
928.2.cc \(\chi_{928}(45, \cdot)\) 928.2.cc.a 2832 24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(928))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(928)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(232))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(464))\)\(^{\oplus 2}\)