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

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

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

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