Properties

Label 1900.4
Level 1900
Weight 4
Dimension 172531
Nonzero newspaces 36
Sturm bound 864000
Trace bound 7

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Defining parameters

Level: \( N \) = \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(864000\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1900))\).

Total New Old
Modular forms 326520 173927 152593
Cusp forms 321480 172531 148949
Eisenstein series 5040 1396 3644

Trace form

\( 172531 q - 105 q^{2} + 16 q^{3} - 97 q^{4} - 218 q^{5} - 121 q^{6} - 64 q^{7} - 273 q^{8} - 630 q^{9} + O(q^{10}) \) \( 172531 q - 105 q^{2} + 16 q^{3} - 97 q^{4} - 218 q^{5} - 121 q^{6} - 64 q^{7} - 273 q^{8} - 630 q^{9} - 272 q^{10} - 80 q^{11} - 417 q^{12} + 174 q^{13} - 97 q^{14} + 344 q^{15} + 583 q^{16} + 126 q^{17} + 1136 q^{18} + 250 q^{19} + 364 q^{20} - 758 q^{21} + 1343 q^{22} - 706 q^{23} - 117 q^{24} - 1534 q^{25} - 2153 q^{26} - 1679 q^{27} - 2186 q^{28} - 420 q^{29} - 2604 q^{30} - 278 q^{31} - 2940 q^{32} + 168 q^{33} - 1222 q^{34} + 1256 q^{35} - 759 q^{36} + 408 q^{37} - 1728 q^{38} - 1746 q^{39} - 552 q^{40} + 2348 q^{41} + 1613 q^{42} - 470 q^{43} + 2788 q^{44} + 4082 q^{45} + 134 q^{46} + 4148 q^{47} + 5842 q^{48} + 7674 q^{49} + 4268 q^{50} + 3539 q^{51} + 1547 q^{52} - 64 q^{53} + 7200 q^{54} + 1480 q^{55} + 8888 q^{56} + 178 q^{57} + 7414 q^{58} + 1058 q^{59} - 5764 q^{60} + 1556 q^{61} - 5852 q^{62} - 1688 q^{63} - 13861 q^{64} - 5078 q^{65} - 11409 q^{66} - 6826 q^{67} - 8612 q^{68} - 17294 q^{69} - 6204 q^{70} - 6172 q^{71} + 260 q^{72} - 2399 q^{73} + 5211 q^{74} - 7384 q^{75} + 8521 q^{76} + 9170 q^{77} + 20525 q^{78} + 12902 q^{79} + 4068 q^{80} + 23669 q^{81} + 23062 q^{82} + 3432 q^{83} + 22787 q^{84} - 7418 q^{85} - 2606 q^{86} - 16436 q^{87} - 7609 q^{88} - 12146 q^{89} - 7132 q^{90} - 15776 q^{91} - 24922 q^{92} - 28124 q^{93} - 22240 q^{94} - 7948 q^{95} + 506 q^{96} + 2778 q^{97} - 13540 q^{98} - 24505 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1900))\)

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
1900.4.a \(\chi_{1900}(1, \cdot)\) 1900.4.a.a 1 1
1900.4.a.b 2
1900.4.a.c 3
1900.4.a.d 4
1900.4.a.e 4
1900.4.a.f 4
1900.4.a.g 5
1900.4.a.h 9
1900.4.a.i 9
1900.4.a.j 9
1900.4.a.k 9
1900.4.a.l 12
1900.4.a.m 14
1900.4.c \(\chi_{1900}(1749, \cdot)\) 1900.4.c.a 2 1
1900.4.c.b 4
1900.4.c.c 6
1900.4.c.d 8
1900.4.c.e 8
1900.4.c.f 8
1900.4.c.g 10
1900.4.c.h 18
1900.4.c.i 18
1900.4.d \(\chi_{1900}(1899, \cdot)\) n/a 536 1
1900.4.f \(\chi_{1900}(151, \cdot)\) n/a 564 1
1900.4.i \(\chi_{1900}(201, \cdot)\) n/a 190 2
1900.4.k \(\chi_{1900}(343, \cdot)\) n/a 972 2
1900.4.l \(\chi_{1900}(493, \cdot)\) n/a 180 2
1900.4.n \(\chi_{1900}(381, \cdot)\) n/a 544 4
1900.4.o \(\chi_{1900}(1551, \cdot)\) n/a 1128 2
1900.4.s \(\chi_{1900}(49, \cdot)\) n/a 180 2
1900.4.t \(\chi_{1900}(1399, \cdot)\) n/a 1072 2
1900.4.v \(\chi_{1900}(101, \cdot)\) n/a 570 6
1900.4.x \(\chi_{1900}(531, \cdot)\) n/a 3584 4
1900.4.z \(\chi_{1900}(229, \cdot)\) n/a 536 4
1900.4.bc \(\chi_{1900}(379, \cdot)\) n/a 3584 4
1900.4.bd \(\chi_{1900}(7, \cdot)\) n/a 2144 4
1900.4.bg \(\chi_{1900}(293, \cdot)\) n/a 360 4
1900.4.bh \(\chi_{1900}(121, \cdot)\) n/a 1200 8
1900.4.bk \(\chi_{1900}(299, \cdot)\) n/a 3216 6
1900.4.bm \(\chi_{1900}(149, \cdot)\) n/a 540 6
1900.4.bn \(\chi_{1900}(51, \cdot)\) n/a 3384 6
1900.4.bq \(\chi_{1900}(37, \cdot)\) n/a 1200 8
1900.4.br \(\chi_{1900}(267, \cdot)\) n/a 6480 8
1900.4.bt \(\chi_{1900}(429, \cdot)\) n/a 1200 8
1900.4.bw \(\chi_{1900}(179, \cdot)\) n/a 7168 8
1900.4.by \(\chi_{1900}(31, \cdot)\) n/a 7168 8
1900.4.cb \(\chi_{1900}(193, \cdot)\) n/a 1080 12
1900.4.cd \(\chi_{1900}(43, \cdot)\) n/a 6432 12
1900.4.ce \(\chi_{1900}(61, \cdot)\) n/a 3600 24
1900.4.cf \(\chi_{1900}(217, \cdot)\) n/a 2400 16
1900.4.ci \(\chi_{1900}(83, \cdot)\) n/a 14336 16
1900.4.cj \(\chi_{1900}(59, \cdot)\) n/a 21504 24
1900.4.cn \(\chi_{1900}(71, \cdot)\) n/a 21504 24
1900.4.co \(\chi_{1900}(9, \cdot)\) n/a 3600 24
1900.4.cq \(\chi_{1900}(23, \cdot)\) n/a 43008 48
1900.4.cs \(\chi_{1900}(13, \cdot)\) n/a 7200 48

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1900))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1900)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(380))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(475))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(950))\)\(^{\oplus 2}\)