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Properties

Label 984.2
Level 984
Weight 2
Dimension 11170
Nonzero newspaces 24
Newform subspaces 59
Sturm bound 107520
Trace bound 8

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Defining parameters

Level: \( N \) = \( 984 = 2^{3} \cdot 3 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Newform subspaces: \( 59 \)
Sturm bound: \(107520\)
Trace bound: \(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(984))\).

Total New Old
Modular forms 27840 11482 16358
Cusp forms 25921 11170 14751
Eisenstein series 1919 312 1607

Trace form

\( 11170 q + 4 q^{2} - 34 q^{3} - 72 q^{4} + 4 q^{5} - 44 q^{6} - 72 q^{7} - 8 q^{8} - 74 q^{9} + O(q^{10}) \) \( 11170 q + 4 q^{2} - 34 q^{3} - 72 q^{4} + 4 q^{5} - 44 q^{6} - 72 q^{7} - 8 q^{8} - 74 q^{9} - 88 q^{10} - 8 q^{11} - 56 q^{12} + 4 q^{13} - 8 q^{14} - 52 q^{15} - 80 q^{16} + 4 q^{17} - 28 q^{18} - 80 q^{19} + 16 q^{20} - 64 q^{22} - 16 q^{24} - 142 q^{25} + 16 q^{26} - 58 q^{27} - 80 q^{28} - 12 q^{29} - 32 q^{30} - 104 q^{31} - 16 q^{32} - 88 q^{33} - 120 q^{34} - 48 q^{36} - 12 q^{37} - 16 q^{38} - 28 q^{39} - 96 q^{40} + 2 q^{41} - 88 q^{42} - 48 q^{43} + 4 q^{45} - 64 q^{46} + 48 q^{47} - 24 q^{48} - 162 q^{49} + 4 q^{50} - 4 q^{51} - 112 q^{52} + 4 q^{53} - 52 q^{54} - 64 q^{55} + 16 q^{56} - 96 q^{57} - 56 q^{58} - 8 q^{59} - 40 q^{60} + 4 q^{61} + 8 q^{62} - 48 q^{63} - 48 q^{64} - 20 q^{65} - 56 q^{66} - 8 q^{67} + 64 q^{69} - 64 q^{70} + 96 q^{71} - 64 q^{72} - 4 q^{73} - 32 q^{74} + 98 q^{75} - 32 q^{76} + 160 q^{77} - 56 q^{78} + 56 q^{79} - 38 q^{81} - 44 q^{82} + 168 q^{83} - 24 q^{84} + 348 q^{85} + 16 q^{86} + 76 q^{87} - 112 q^{88} + 212 q^{89} - 32 q^{90} + 240 q^{91} + 96 q^{93} - 128 q^{94} + 176 q^{95} - 88 q^{96} + 44 q^{97} - 12 q^{98} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(984))\)

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
984.2.a \(\chi_{984}(1, \cdot)\) 984.2.a.a 1 1
984.2.a.b 1
984.2.a.c 1
984.2.a.d 1
984.2.a.e 2
984.2.a.f 3
984.2.a.g 3
984.2.a.h 3
984.2.a.i 5
984.2.d \(\chi_{984}(575, \cdot)\) None 0 1
984.2.e \(\chi_{984}(901, \cdot)\) 984.2.e.a 42 1
984.2.e.b 42
984.2.f \(\chi_{984}(493, \cdot)\) 984.2.f.a 40 1
984.2.f.b 40
984.2.g \(\chi_{984}(983, \cdot)\) None 0 1
984.2.j \(\chi_{984}(409, \cdot)\) 984.2.j.a 2 1
984.2.j.b 8
984.2.j.c 12
984.2.k \(\chi_{984}(83, \cdot)\) 984.2.k.a 160 1
984.2.p \(\chi_{984}(491, \cdot)\) 984.2.p.a 2 1
984.2.p.b 2
984.2.p.c 160
984.2.s \(\chi_{984}(155, \cdot)\) 984.2.s.a 4 2
984.2.s.b 4
984.2.s.c 320
984.2.t \(\chi_{984}(73, \cdot)\) 984.2.t.a 4 2
984.2.t.b 16
984.2.t.c 20
984.2.w \(\chi_{984}(647, \cdot)\) None 0 2
984.2.x \(\chi_{984}(565, \cdot)\) 984.2.x.a 168 2
984.2.y \(\chi_{984}(385, \cdot)\) 984.2.y.a 4 4
984.2.y.b 4
984.2.y.c 8
984.2.y.d 8
984.2.y.e 20
984.2.y.f 20
984.2.y.g 24
984.2.bd \(\chi_{984}(413, \cdot)\) 984.2.bd.a 656 4
984.2.be \(\chi_{984}(137, \cdot)\) 984.2.be.a 84 4
984.2.be.b 84
984.2.bf \(\chi_{984}(331, \cdot)\) 984.2.bf.a 336 4
984.2.bg \(\chi_{984}(55, \cdot)\) None 0 4
984.2.bh \(\chi_{984}(107, \cdot)\) 984.2.bh.a 8 4
984.2.bh.b 8
984.2.bh.c 640
984.2.bm \(\chi_{984}(59, \cdot)\) 984.2.bm.a 8 4
984.2.bm.b 8
984.2.bm.c 640
984.2.bn \(\chi_{984}(25, \cdot)\) 984.2.bn.a 40 4
984.2.bn.b 48
984.2.bq \(\chi_{984}(23, \cdot)\) None 0 4
984.2.br \(\chi_{984}(37, \cdot)\) 984.2.br.a 336 4
984.2.bs \(\chi_{984}(277, \cdot)\) 984.2.bs.a 168 4
984.2.bs.b 168
984.2.bt \(\chi_{984}(119, \cdot)\) None 0 4
984.2.bw \(\chi_{984}(61, \cdot)\) 984.2.bw.a 672 8
984.2.bx \(\chi_{984}(143, \cdot)\) None 0 8
984.2.ca \(\chi_{984}(49, \cdot)\) 984.2.ca.a 80 8
984.2.ca.b 80
984.2.cb \(\chi_{984}(131, \cdot)\) 984.2.cb.a 16 8
984.2.cb.b 16
984.2.cb.c 1280
984.2.ce \(\chi_{984}(7, \cdot)\) None 0 16
984.2.cf \(\chi_{984}(19, \cdot)\) 984.2.cf.a 1344 16
984.2.cg \(\chi_{984}(17, \cdot)\) 984.2.cg.a 336 16
984.2.cg.b 336
984.2.ch \(\chi_{984}(29, \cdot)\) 984.2.ch.a 2624 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(984))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(984)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(123))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(246))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(328))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(492))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(984))\)\(^{\oplus 1}\)