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Properties

Label 992.2
Level 992
Weight 2
Dimension 16954
Nonzero newspaces 24
Newform subspaces 55
Sturm bound 122880
Trace bound 13

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Defining parameters

Level: \( N \) = \( 992 = 2^{5} \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Newform subspaces: \( 55 \)
Sturm bound: \(122880\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(992))\).

Total New Old
Modular forms 31680 17534 14146
Cusp forms 29761 16954 12807
Eisenstein series 1919 580 1339

Trace form

\( 16954 q - 112 q^{2} - 82 q^{3} - 112 q^{4} - 108 q^{5} - 112 q^{6} - 82 q^{7} - 112 q^{8} - 166 q^{9} + O(q^{10}) \) \( 16954 q - 112 q^{2} - 82 q^{3} - 112 q^{4} - 108 q^{5} - 112 q^{6} - 82 q^{7} - 112 q^{8} - 166 q^{9} - 128 q^{10} - 82 q^{11} - 144 q^{12} - 124 q^{13} - 144 q^{14} - 90 q^{15} - 152 q^{16} - 64 q^{17} - 152 q^{18} - 82 q^{19} - 144 q^{20} - 112 q^{21} - 136 q^{22} - 98 q^{23} - 88 q^{24} - 170 q^{25} - 72 q^{26} - 130 q^{27} - 72 q^{28} - 92 q^{29} - 48 q^{30} - 106 q^{31} - 192 q^{32} - 284 q^{33} - 88 q^{34} - 130 q^{35} - 56 q^{36} - 108 q^{37} - 128 q^{38} - 130 q^{39} - 136 q^{40} - 192 q^{41} - 152 q^{42} - 98 q^{43} - 192 q^{44} - 148 q^{45} - 176 q^{46} - 90 q^{47} - 216 q^{48} - 46 q^{49} - 192 q^{50} - 74 q^{51} - 128 q^{52} - 172 q^{53} - 136 q^{54} - 18 q^{55} - 136 q^{56} - 172 q^{57} - 104 q^{58} - 18 q^{59} - 104 q^{60} - 156 q^{61} - 96 q^{62} - 84 q^{63} - 40 q^{64} - 260 q^{65} - 64 q^{66} - 2 q^{67} - 152 q^{68} - 176 q^{69} - 88 q^{70} - 18 q^{71} - 160 q^{72} - 160 q^{73} - 144 q^{74} - 58 q^{75} - 112 q^{76} - 144 q^{77} - 192 q^{78} - 90 q^{79} - 104 q^{80} - 78 q^{81} - 112 q^{82} - 162 q^{83} - 152 q^{84} - 144 q^{85} - 72 q^{86} - 194 q^{87} - 120 q^{88} - 192 q^{89} - 136 q^{90} - 178 q^{91} - 40 q^{92} - 104 q^{93} - 256 q^{94} - 202 q^{95} - 120 q^{96} - 320 q^{97} - 72 q^{98} - 186 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(992))\)

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
992.2.a \(\chi_{992}(1, \cdot)\) 992.2.a.a 2 1
992.2.a.b 2
992.2.a.c 3
992.2.a.d 3
992.2.a.e 4
992.2.a.f 4
992.2.a.g 6
992.2.a.h 6
992.2.b \(\chi_{992}(495, \cdot)\) 992.2.b.a 6 1
992.2.b.b 24
992.2.c \(\chi_{992}(497, \cdot)\) 992.2.c.a 12 1
992.2.c.b 18
992.2.h \(\chi_{992}(991, \cdot)\) 992.2.h.a 32 1
992.2.i \(\chi_{992}(129, \cdot)\) 992.2.i.a 2 2
992.2.i.b 2
992.2.i.c 4
992.2.i.d 4
992.2.i.e 4
992.2.i.f 4
992.2.i.g 8
992.2.i.h 10
992.2.i.i 10
992.2.i.j 16
992.2.k \(\chi_{992}(249, \cdot)\) None 0 2
992.2.m \(\chi_{992}(247, \cdot)\) None 0 2
992.2.n \(\chi_{992}(33, \cdot)\) 992.2.n.a 32 4
992.2.n.b 32
992.2.n.c 32
992.2.n.d 32
992.2.o \(\chi_{992}(223, \cdot)\) 992.2.o.a 64 2
992.2.t \(\chi_{992}(273, \cdot)\) 992.2.t.a 4 2
992.2.t.b 56
992.2.u \(\chi_{992}(367, \cdot)\) 992.2.u.a 4 2
992.2.u.b 4
992.2.u.c 4
992.2.u.d 48
992.2.v \(\chi_{992}(125, \cdot)\) 992.2.v.a 4 4
992.2.v.b 224
992.2.v.c 252
992.2.w \(\chi_{992}(123, \cdot)\) 992.2.w.a 24 4
992.2.w.b 480
992.2.bb \(\chi_{992}(511, \cdot)\) 992.2.bb.a 128 4
992.2.bc \(\chi_{992}(529, \cdot)\) 992.2.bc.a 120 4
992.2.bd \(\chi_{992}(15, \cdot)\) 992.2.bd.a 120 4
992.2.bh \(\chi_{992}(119, \cdot)\) None 0 4
992.2.bj \(\chi_{992}(25, \cdot)\) None 0 4
992.2.bk \(\chi_{992}(193, \cdot)\) 992.2.bk.a 64 8
992.2.bk.b 64
992.2.bk.c 64
992.2.bk.d 64
992.2.bl \(\chi_{992}(23, \cdot)\) None 0 8
992.2.bn \(\chi_{992}(233, \cdot)\) None 0 8
992.2.bp \(\chi_{992}(99, \cdot)\) 992.2.bp.a 1008 8
992.2.bq \(\chi_{992}(5, \cdot)\) 992.2.bq.a 1008 8
992.2.bv \(\chi_{992}(79, \cdot)\) 992.2.bv.a 240 8
992.2.bw \(\chi_{992}(49, \cdot)\) 992.2.bw.a 240 8
992.2.bx \(\chi_{992}(127, \cdot)\) 992.2.bx.a 256 8
992.2.cc \(\chi_{992}(27, \cdot)\) 992.2.cc.a 2016 16
992.2.cd \(\chi_{992}(101, \cdot)\) 992.2.cd.a 2016 16
992.2.ce \(\chi_{992}(9, \cdot)\) None 0 16
992.2.cg \(\chi_{992}(55, \cdot)\) None 0 16
992.2.ck \(\chi_{992}(45, \cdot)\) 992.2.ck.a 4032 32
992.2.cl \(\chi_{992}(3, \cdot)\) 992.2.cl.a 4032 32

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(992))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(992)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(248))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(496))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(992))\)\(^{\oplus 1}\)