Properties

Label 1050.2
Level 1050
Weight 2
Dimension 6362
Nonzero newspaces 24
Sturm bound 115200
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(115200\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1050))\).

Total New Old
Modular forms 30144 6362 23782
Cusp forms 27457 6362 21095
Eisenstein series 2687 0 2687

Trace form

\(6362q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 16q^{3} \) \(\mathstrut -\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 20q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut -\mathstrut 14q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6362q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 16q^{3} \) \(\mathstrut -\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 20q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut -\mathstrut 14q^{9} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut -\mathstrut 32q^{11} \) \(\mathstrut +\mathstrut 16q^{12} \) \(\mathstrut -\mathstrut 36q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut -\mathstrut 6q^{16} \) \(\mathstrut +\mathstrut 56q^{17} \) \(\mathstrut +\mathstrut 58q^{18} \) \(\mathstrut +\mathstrut 88q^{19} \) \(\mathstrut +\mathstrut 16q^{20} \) \(\mathstrut +\mathstrut 42q^{21} \) \(\mathstrut +\mathstrut 120q^{22} \) \(\mathstrut +\mathstrut 100q^{23} \) \(\mathstrut +\mathstrut 32q^{24} \) \(\mathstrut +\mathstrut 220q^{25} \) \(\mathstrut +\mathstrut 80q^{26} \) \(\mathstrut +\mathstrut 128q^{27} \) \(\mathstrut +\mathstrut 100q^{28} \) \(\mathstrut +\mathstrut 244q^{29} \) \(\mathstrut +\mathstrut 112q^{30} \) \(\mathstrut +\mathstrut 184q^{31} \) \(\mathstrut +\mathstrut 14q^{32} \) \(\mathstrut +\mathstrut 256q^{33} \) \(\mathstrut +\mathstrut 224q^{34} \) \(\mathstrut +\mathstrut 152q^{35} \) \(\mathstrut +\mathstrut 82q^{36} \) \(\mathstrut +\mathstrut 280q^{37} \) \(\mathstrut +\mathstrut 132q^{38} \) \(\mathstrut +\mathstrut 320q^{39} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut +\mathstrut 132q^{41} \) \(\mathstrut +\mathstrut 122q^{42} \) \(\mathstrut +\mathstrut 264q^{43} \) \(\mathstrut +\mathstrut 32q^{44} \) \(\mathstrut +\mathstrut 212q^{45} \) \(\mathstrut +\mathstrut 96q^{46} \) \(\mathstrut +\mathstrut 124q^{47} \) \(\mathstrut +\mathstrut 16q^{48} \) \(\mathstrut -\mathstrut 34q^{49} \) \(\mathstrut -\mathstrut 36q^{50} \) \(\mathstrut +\mathstrut 72q^{51} \) \(\mathstrut -\mathstrut 12q^{52} \) \(\mathstrut +\mathstrut 12q^{53} \) \(\mathstrut +\mathstrut 4q^{54} \) \(\mathstrut +\mathstrut 96q^{55} \) \(\mathstrut -\mathstrut 20q^{56} \) \(\mathstrut +\mathstrut 108q^{57} \) \(\mathstrut -\mathstrut 104q^{58} \) \(\mathstrut +\mathstrut 104q^{59} \) \(\mathstrut -\mathstrut 64q^{60} \) \(\mathstrut +\mathstrut 84q^{61} \) \(\mathstrut -\mathstrut 120q^{62} \) \(\mathstrut -\mathstrut 20q^{63} \) \(\mathstrut -\mathstrut 10q^{64} \) \(\mathstrut -\mathstrut 4q^{65} \) \(\mathstrut -\mathstrut 96q^{66} \) \(\mathstrut +\mathstrut 144q^{67} \) \(\mathstrut -\mathstrut 24q^{68} \) \(\mathstrut -\mathstrut 192q^{69} \) \(\mathstrut -\mathstrut 48q^{70} \) \(\mathstrut +\mathstrut 72q^{71} \) \(\mathstrut -\mathstrut 50q^{72} \) \(\mathstrut +\mathstrut 112q^{73} \) \(\mathstrut -\mathstrut 104q^{74} \) \(\mathstrut -\mathstrut 232q^{75} \) \(\mathstrut -\mathstrut 8q^{76} \) \(\mathstrut +\mathstrut 84q^{77} \) \(\mathstrut -\mathstrut 260q^{78} \) \(\mathstrut +\mathstrut 136q^{79} \) \(\mathstrut -\mathstrut 20q^{80} \) \(\mathstrut -\mathstrut 94q^{81} \) \(\mathstrut -\mathstrut 196q^{82} \) \(\mathstrut +\mathstrut 32q^{83} \) \(\mathstrut -\mathstrut 94q^{84} \) \(\mathstrut +\mathstrut 28q^{85} \) \(\mathstrut -\mathstrut 100q^{86} \) \(\mathstrut -\mathstrut 280q^{87} \) \(\mathstrut -\mathstrut 52q^{88} \) \(\mathstrut -\mathstrut 104q^{89} \) \(\mathstrut -\mathstrut 204q^{90} \) \(\mathstrut -\mathstrut 112q^{91} \) \(\mathstrut -\mathstrut 72q^{92} \) \(\mathstrut -\mathstrut 324q^{93} \) \(\mathstrut -\mathstrut 232q^{94} \) \(\mathstrut -\mathstrut 32q^{95} \) \(\mathstrut -\mathstrut 24q^{96} \) \(\mathstrut -\mathstrut 160q^{97} \) \(\mathstrut -\mathstrut 78q^{98} \) \(\mathstrut -\mathstrut 424q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1050))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1050.2.a \(\chi_{1050}(1, \cdot)\) 1050.2.a.a 1 1
1050.2.a.b 1
1050.2.a.c 1
1050.2.a.d 1
1050.2.a.e 1
1050.2.a.f 1
1050.2.a.g 1
1050.2.a.h 1
1050.2.a.i 1
1050.2.a.j 1
1050.2.a.k 1
1050.2.a.l 1
1050.2.a.m 1
1050.2.a.n 1
1050.2.a.o 1
1050.2.a.p 1
1050.2.a.q 1
1050.2.a.r 1
1050.2.b \(\chi_{1050}(251, \cdot)\) 1050.2.b.a 4 1
1050.2.b.b 4
1050.2.b.c 4
1050.2.b.d 12
1050.2.b.e 12
1050.2.b.f 16
1050.2.d \(\chi_{1050}(1049, \cdot)\) 1050.2.d.a 4 1
1050.2.d.b 4
1050.2.d.c 4
1050.2.d.d 4
1050.2.d.e 4
1050.2.d.f 4
1050.2.d.g 12
1050.2.d.h 12
1050.2.g \(\chi_{1050}(799, \cdot)\) 1050.2.g.a 2 1
1050.2.g.b 2
1050.2.g.c 2
1050.2.g.d 2
1050.2.g.e 2
1050.2.g.f 2
1050.2.g.g 2
1050.2.g.h 2
1050.2.g.i 2
1050.2.g.j 2
1050.2.i \(\chi_{1050}(151, \cdot)\) 1050.2.i.a 2 2
1050.2.i.b 2
1050.2.i.c 2
1050.2.i.d 2
1050.2.i.e 2
1050.2.i.f 2
1050.2.i.g 2
1050.2.i.h 2
1050.2.i.i 2
1050.2.i.j 2
1050.2.i.k 2
1050.2.i.l 2
1050.2.i.m 2
1050.2.i.n 2
1050.2.i.o 2
1050.2.i.p 2
1050.2.i.q 2
1050.2.i.r 2
1050.2.i.s 2
1050.2.i.t 2
1050.2.i.u 6
1050.2.i.v 6
1050.2.j \(\chi_{1050}(407, \cdot)\) 1050.2.j.a 8 2
1050.2.j.b 8
1050.2.j.c 12
1050.2.j.d 12
1050.2.j.e 16
1050.2.j.f 16
1050.2.m \(\chi_{1050}(307, \cdot)\) 1050.2.m.a 8 2
1050.2.m.b 8
1050.2.m.c 8
1050.2.m.d 8
1050.2.m.e 8
1050.2.m.f 8
1050.2.n \(\chi_{1050}(211, \cdot)\) n/a 128 4
1050.2.o \(\chi_{1050}(499, \cdot)\) 1050.2.o.a 4 2
1050.2.o.b 4
1050.2.o.c 4
1050.2.o.d 4
1050.2.o.e 4
1050.2.o.f 4
1050.2.o.g 4
1050.2.o.h 4
1050.2.o.i 4
1050.2.o.j 4
1050.2.o.k 4
1050.2.o.l 4
1050.2.s \(\chi_{1050}(101, \cdot)\) 1050.2.s.a 4 2
1050.2.s.b 4
1050.2.s.c 4
1050.2.s.d 8
1050.2.s.e 8
1050.2.s.f 12
1050.2.s.g 12
1050.2.s.h 16
1050.2.s.i 16
1050.2.s.j 16
1050.2.u \(\chi_{1050}(299, \cdot)\) 1050.2.u.a 4 2
1050.2.u.b 4
1050.2.u.c 4
1050.2.u.d 4
1050.2.u.e 12
1050.2.u.f 12
1050.2.u.g 12
1050.2.u.h 12
1050.2.u.i 16
1050.2.u.j 16
1050.2.w \(\chi_{1050}(169, \cdot)\) n/a 112 4
1050.2.z \(\chi_{1050}(209, \cdot)\) n/a 320 4
1050.2.bb \(\chi_{1050}(41, \cdot)\) n/a 320 4
1050.2.bc \(\chi_{1050}(157, \cdot)\) 1050.2.bc.a 8 4
1050.2.bc.b 8
1050.2.bc.c 8
1050.2.bc.d 8
1050.2.bc.e 16
1050.2.bc.f 16
1050.2.bc.g 16
1050.2.bc.h 16
1050.2.bf \(\chi_{1050}(107, \cdot)\) n/a 192 4
1050.2.bg \(\chi_{1050}(121, \cdot)\) n/a 320 8
1050.2.bh \(\chi_{1050}(13, \cdot)\) n/a 320 8
1050.2.bk \(\chi_{1050}(113, \cdot)\) n/a 480 8
1050.2.bl \(\chi_{1050}(59, \cdot)\) n/a 640 8
1050.2.bn \(\chi_{1050}(131, \cdot)\) n/a 640 8
1050.2.br \(\chi_{1050}(79, \cdot)\) n/a 320 8
1050.2.bs \(\chi_{1050}(23, \cdot)\) n/a 1280 16
1050.2.bv \(\chi_{1050}(73, \cdot)\) n/a 640 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1050))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1050)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(350))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(525))\)\(^{\oplus 2}\)