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Properties

Label 1050.4
Level 1050
Weight 4
Dimension 19078
Nonzero newspaces 24
Sturm bound 230400
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(230400\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1050))\).

Total New Old
Modular forms 87744 19078 68666
Cusp forms 85056 19078 65978
Eisenstein series 2688 0 2688

Trace form

\( 19078 q - 12 q^{2} + 26 q^{3} + 24 q^{4} + 20 q^{5} + 56 q^{6} + 128 q^{7} - 48 q^{8} + 12 q^{9} + O(q^{10}) \) \( 19078 q - 12 q^{2} + 26 q^{3} + 24 q^{4} + 20 q^{5} + 56 q^{6} + 128 q^{7} - 48 q^{8} + 12 q^{9} - 104 q^{10} + 116 q^{11} - 152 q^{12} - 368 q^{13} - 32 q^{14} - 512 q^{15} - 416 q^{16} + 1528 q^{17} + 20 q^{18} + 760 q^{19} - 64 q^{20} + 136 q^{21} - 1680 q^{22} - 2140 q^{23} - 672 q^{24} - 2860 q^{25} + 2128 q^{26} + 524 q^{27} + 320 q^{28} - 1996 q^{29} - 288 q^{30} - 1296 q^{31} + 448 q^{32} - 886 q^{33} + 1504 q^{34} - 1328 q^{35} + 8 q^{36} - 2716 q^{37} - 2952 q^{38} + 740 q^{39} - 288 q^{40} + 1740 q^{41} + 380 q^{42} - 4632 q^{43} + 1360 q^{44} - 1788 q^{45} + 2096 q^{46} + 3320 q^{47} - 320 q^{48} + 3694 q^{49} + 504 q^{50} + 466 q^{51} + 3040 q^{52} - 3636 q^{53} + 936 q^{54} + 7456 q^{55} - 352 q^{56} + 11904 q^{57} + 7872 q^{58} + 14560 q^{59} - 3264 q^{60} - 1164 q^{61} + 1872 q^{62} - 3842 q^{63} - 384 q^{64} - 764 q^{65} - 640 q^{66} - 19592 q^{67} - 4128 q^{68} - 3832 q^{69} - 2688 q^{70} - 11208 q^{71} + 496 q^{72} - 12884 q^{73} - 3232 q^{74} + 18768 q^{75} - 1904 q^{76} - 7884 q^{77} + 1432 q^{78} - 1328 q^{79} + 320 q^{80} - 10236 q^{81} + 6840 q^{82} + 25000 q^{83} + 1104 q^{84} + 24788 q^{85} + 7624 q^{86} - 10608 q^{87} + 4128 q^{88} + 13616 q^{89} - 19544 q^{90} + 2728 q^{91} + 7296 q^{92} - 18062 q^{93} + 12800 q^{94} - 14752 q^{95} + 640 q^{96} - 30872 q^{97} - 636 q^{98} + 19884 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1050))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1050.4.a \(\chi_{1050}(1, \cdot)\) 1050.4.a.a 1 1
1050.4.a.b 1
1050.4.a.c 1
1050.4.a.d 1
1050.4.a.e 1
1050.4.a.f 1
1050.4.a.g 1
1050.4.a.h 1
1050.4.a.i 1
1050.4.a.j 1
1050.4.a.k 1
1050.4.a.l 1
1050.4.a.m 1
1050.4.a.n 1
1050.4.a.o 1
1050.4.a.p 1
1050.4.a.q 1
1050.4.a.r 1
1050.4.a.s 1
1050.4.a.t 1
1050.4.a.u 1
1050.4.a.v 1
1050.4.a.w 1
1050.4.a.x 1
1050.4.a.y 2
1050.4.a.z 2
1050.4.a.ba 2
1050.4.a.bb 2
1050.4.a.bc 2
1050.4.a.bd 2
1050.4.a.be 2
1050.4.a.bf 2
1050.4.a.bg 2
1050.4.a.bh 2
1050.4.a.bi 2
1050.4.a.bj 3
1050.4.a.bk 3
1050.4.a.bl 3
1050.4.a.bm 3
1050.4.b \(\chi_{1050}(251, \cdot)\) n/a 152 1
1050.4.d \(\chi_{1050}(1049, \cdot)\) n/a 144 1
1050.4.g \(\chi_{1050}(799, \cdot)\) 1050.4.g.a 2 1
1050.4.g.b 2
1050.4.g.c 2
1050.4.g.d 2
1050.4.g.e 2
1050.4.g.f 2
1050.4.g.g 2
1050.4.g.h 2
1050.4.g.i 2
1050.4.g.j 2
1050.4.g.k 2
1050.4.g.l 2
1050.4.g.m 2
1050.4.g.n 2
1050.4.g.o 2
1050.4.g.p 2
1050.4.g.q 2
1050.4.g.r 2
1050.4.g.s 4
1050.4.g.t 4
1050.4.g.u 4
1050.4.g.v 4
1050.4.i \(\chi_{1050}(151, \cdot)\) n/a 152 2
1050.4.j \(\chi_{1050}(407, \cdot)\) n/a 216 2
1050.4.m \(\chi_{1050}(307, \cdot)\) n/a 144 2
1050.4.n \(\chi_{1050}(211, \cdot)\) n/a 352 4
1050.4.o \(\chi_{1050}(499, \cdot)\) n/a 144 2
1050.4.s \(\chi_{1050}(101, \cdot)\) n/a 304 2
1050.4.u \(\chi_{1050}(299, \cdot)\) n/a 288 2
1050.4.w \(\chi_{1050}(169, \cdot)\) n/a 368 4
1050.4.z \(\chi_{1050}(209, \cdot)\) n/a 960 4
1050.4.bb \(\chi_{1050}(41, \cdot)\) n/a 960 4
1050.4.bc \(\chi_{1050}(157, \cdot)\) n/a 288 4
1050.4.bf \(\chi_{1050}(107, \cdot)\) n/a 576 4
1050.4.bg \(\chi_{1050}(121, \cdot)\) n/a 960 8
1050.4.bh \(\chi_{1050}(13, \cdot)\) n/a 960 8
1050.4.bk \(\chi_{1050}(113, \cdot)\) n/a 1440 8
1050.4.bl \(\chi_{1050}(59, \cdot)\) n/a 1920 8
1050.4.bn \(\chi_{1050}(131, \cdot)\) n/a 1920 8
1050.4.br \(\chi_{1050}(79, \cdot)\) n/a 960 8
1050.4.bs \(\chi_{1050}(23, \cdot)\) n/a 3840 16
1050.4.bv \(\chi_{1050}(73, \cdot)\) n/a 1920 16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1050))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1050)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(350))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(525))\)\(^{\oplus 2}\)