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Properties

Label 1950.4
Level 1950
Weight 4
Dimension 68848
Nonzero newspaces 40
Sturm bound 806400
Trace bound 18

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Defining parameters

Level: \( N \) = \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(806400\)
Trace bound: \(18\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1950))\).

Total New Old
Modular forms 305088 68848 236240
Cusp forms 299712 68848 230864
Eisenstein series 5376 0 5376

Trace form

\( 68848 q - 12 q^{2} + 38 q^{3} + 24 q^{4} + 20 q^{5} + 20 q^{6} - 80 q^{7} - 96 q^{8} + 54 q^{9} + O(q^{10}) \) \( 68848 q - 12 q^{2} + 38 q^{3} + 24 q^{4} + 20 q^{5} + 20 q^{6} - 80 q^{7} - 96 q^{8} + 54 q^{9} - 104 q^{10} + 440 q^{11} - 56 q^{12} + 386 q^{13} + 176 q^{14} - 512 q^{15} - 416 q^{16} + 1042 q^{17} + 80 q^{18} - 224 q^{19} - 64 q^{20} + 1448 q^{21} - 1680 q^{22} - 1768 q^{23} - 624 q^{24} - 5548 q^{25} - 532 q^{26} - 1870 q^{27} - 704 q^{28} - 934 q^{29} + 720 q^{30} + 2040 q^{31} + 448 q^{32} + 4448 q^{33} + 7216 q^{34} + 7136 q^{35} + 1496 q^{36} + 5294 q^{37} + 1488 q^{38} + 310 q^{39} - 288 q^{40} + 234 q^{41} - 5864 q^{42} - 12696 q^{43} - 3680 q^{44} - 7260 q^{45} - 7648 q^{46} - 7288 q^{47} - 416 q^{48} - 4854 q^{49} + 4008 q^{50} + 21196 q^{51} + 5024 q^{52} + 19128 q^{53} + 12348 q^{54} + 8176 q^{55} + 832 q^{56} + 2124 q^{57} + 2076 q^{58} - 8096 q^{59} - 7488 q^{60} - 12990 q^{61} - 24144 q^{62} - 29332 q^{63} - 2304 q^{64} - 21430 q^{65} - 19456 q^{66} - 36560 q^{67} - 6360 q^{68} - 18292 q^{69} - 15168 q^{70} - 9552 q^{71} - 1520 q^{72} + 5404 q^{73} + 2732 q^{74} + 33552 q^{75} + 5248 q^{76} + 31680 q^{77} + 27308 q^{78} + 33616 q^{79} + 4544 q^{80} + 21462 q^{81} + 16764 q^{82} + 8728 q^{83} + 1728 q^{84} + 8372 q^{85} + 9808 q^{86} + 10932 q^{87} + 4800 q^{88} + 16592 q^{89} - 9368 q^{90} + 10912 q^{91} + 9408 q^{92} - 812 q^{93} + 20240 q^{94} - 14752 q^{95} - 704 q^{96} - 21548 q^{97} - 5388 q^{98} - 1440 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1950))\)

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
1950.4.a \(\chi_{1950}(1, \cdot)\) 1950.4.a.a 1 1
1950.4.a.b 1
1950.4.a.c 1
1950.4.a.d 1
1950.4.a.e 1
1950.4.a.f 1
1950.4.a.g 1
1950.4.a.h 1
1950.4.a.i 1
1950.4.a.j 1
1950.4.a.k 1
1950.4.a.l 1
1950.4.a.m 1
1950.4.a.n 1
1950.4.a.o 1
1950.4.a.p 1
1950.4.a.q 1
1950.4.a.r 2
1950.4.a.s 2
1950.4.a.t 2
1950.4.a.u 2
1950.4.a.v 2
1950.4.a.w 2
1950.4.a.x 2
1950.4.a.y 2
1950.4.a.z 2
1950.4.a.ba 3
1950.4.a.bb 3
1950.4.a.bc 3
1950.4.a.bd 3
1950.4.a.be 3
1950.4.a.bf 3
1950.4.a.bg 3
1950.4.a.bh 3
1950.4.a.bi 3
1950.4.a.bj 4
1950.4.a.bk 4
1950.4.a.bl 4
1950.4.a.bm 4
1950.4.a.bn 4
1950.4.a.bo 4
1950.4.a.bp 4
1950.4.a.bq 4
1950.4.a.br 5
1950.4.a.bs 5
1950.4.a.bt 5
1950.4.a.bu 5
1950.4.b \(\chi_{1950}(1351, \cdot)\) n/a 134 1
1950.4.e \(\chi_{1950}(1249, \cdot)\) n/a 108 1
1950.4.f \(\chi_{1950}(649, \cdot)\) n/a 124 1
1950.4.i \(\chi_{1950}(451, \cdot)\) n/a 264 2
1950.4.j \(\chi_{1950}(1243, \cdot)\) n/a 252 2
1950.4.l \(\chi_{1950}(443, \cdot)\) n/a 432 2
1950.4.n \(\chi_{1950}(749, \cdot)\) n/a 504 2
1950.4.p \(\chi_{1950}(551, \cdot)\) n/a 532 2
1950.4.s \(\chi_{1950}(857, \cdot)\) n/a 504 2
1950.4.t \(\chi_{1950}(307, \cdot)\) n/a 252 2
1950.4.v \(\chi_{1950}(391, \cdot)\) n/a 720 4
1950.4.y \(\chi_{1950}(49, \cdot)\) n/a 248 2
1950.4.z \(\chi_{1950}(1699, \cdot)\) n/a 256 2
1950.4.bc \(\chi_{1950}(751, \cdot)\) n/a 268 2
1950.4.bd \(\chi_{1950}(79, \cdot)\) n/a 720 4
1950.4.bg \(\chi_{1950}(181, \cdot)\) n/a 832 4
1950.4.bj \(\chi_{1950}(259, \cdot)\) n/a 848 4
1950.4.bl \(\chi_{1950}(7, \cdot)\) n/a 504 4
1950.4.bm \(\chi_{1950}(257, \cdot)\) n/a 1008 4
1950.4.bp \(\chi_{1950}(401, \cdot)\) n/a 1064 4
1950.4.br \(\chi_{1950}(149, \cdot)\) n/a 1008 4
1950.4.bt \(\chi_{1950}(107, \cdot)\) n/a 1008 4
1950.4.bv \(\chi_{1950}(193, \cdot)\) n/a 504 4
1950.4.bw \(\chi_{1950}(61, \cdot)\) n/a 1696 8
1950.4.by \(\chi_{1950}(73, \cdot)\) n/a 1680 8
1950.4.bz \(\chi_{1950}(77, \cdot)\) n/a 3360 8
1950.4.cc \(\chi_{1950}(161, \cdot)\) n/a 3360 8
1950.4.ce \(\chi_{1950}(239, \cdot)\) n/a 3360 8
1950.4.cg \(\chi_{1950}(53, \cdot)\) n/a 2880 8
1950.4.ci \(\chi_{1950}(697, \cdot)\) n/a 1680 8
1950.4.cj \(\chi_{1950}(439, \cdot)\) n/a 1696 8
1950.4.cm \(\chi_{1950}(121, \cdot)\) n/a 1664 8
1950.4.cp \(\chi_{1950}(139, \cdot)\) n/a 1664 8
1950.4.cq \(\chi_{1950}(37, \cdot)\) n/a 3360 16
1950.4.cs \(\chi_{1950}(113, \cdot)\) n/a 6720 16
1950.4.cu \(\chi_{1950}(59, \cdot)\) n/a 6720 16
1950.4.cw \(\chi_{1950}(11, \cdot)\) n/a 6720 16
1950.4.cz \(\chi_{1950}(17, \cdot)\) n/a 6720 16
1950.4.da \(\chi_{1950}(67, \cdot)\) n/a 3360 16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1950))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1950)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(325))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(390))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(650))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(975))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1950))\)\(^{\oplus 1}\)