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Properties

Label 3800.2
Level 3800
Weight 2
Dimension 221327
Nonzero newspaces 54
Sturm bound 1728000
Trace bound 15

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Defining parameters

Level: \( N \) = \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 54 \)
Sturm bound: \(1728000\)
Trace bound: \(15\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3800))\).

Total New Old
Modular forms 438048 224115 213933
Cusp forms 425953 221327 204626
Eisenstein series 12095 2788 9307

Trace form

\( 221327 q - 210 q^{2} - 210 q^{3} - 210 q^{4} - 2 q^{5} - 338 q^{6} - 226 q^{7} - 210 q^{8} - 440 q^{9} + O(q^{10}) \) \( 221327 q - 210 q^{2} - 210 q^{3} - 210 q^{4} - 2 q^{5} - 338 q^{6} - 226 q^{7} - 210 q^{8} - 440 q^{9} - 256 q^{10} - 354 q^{11} - 162 q^{12} - 8 q^{13} - 162 q^{14} - 240 q^{15} - 274 q^{16} - 412 q^{17} - 98 q^{18} - 190 q^{19} - 504 q^{20} + 32 q^{21} - 130 q^{22} - 194 q^{23} - 98 q^{24} - 522 q^{25} - 594 q^{26} - 171 q^{27} - 226 q^{28} - 42 q^{29} - 248 q^{30} - 324 q^{31} - 290 q^{32} - 474 q^{33} - 338 q^{34} - 232 q^{35} - 466 q^{36} + 16 q^{37} - 262 q^{38} - 370 q^{39} - 336 q^{40} - 662 q^{41} - 290 q^{42} - 70 q^{43} - 258 q^{44} + 158 q^{45} - 434 q^{46} - 36 q^{47} - 226 q^{48} - 288 q^{49} - 216 q^{50} - 483 q^{51} - 114 q^{52} + 114 q^{53} - 44 q^{54} - 112 q^{55} - 114 q^{56} - 316 q^{57} - 252 q^{58} - 34 q^{59} - 168 q^{60} - 30 q^{61} + 120 q^{62} - 74 q^{63} + 78 q^{64} - 458 q^{65} - 98 q^{66} - 166 q^{67} + 12 q^{68} + 32 q^{69} - 248 q^{70} - 348 q^{71} - 92 q^{72} - 203 q^{73} - 130 q^{74} - 400 q^{75} - 566 q^{76} - 10 q^{77} - 270 q^{78} - 388 q^{79} - 296 q^{80} - 519 q^{81} - 228 q^{82} - 500 q^{83} - 426 q^{84} - 146 q^{85} - 388 q^{86} - 518 q^{87} - 530 q^{88} - 308 q^{89} - 856 q^{90} - 538 q^{91} - 568 q^{92} - 222 q^{93} - 670 q^{94} - 400 q^{95} - 892 q^{96} - 600 q^{97} - 706 q^{98} - 673 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3800))\)

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
3800.2.a \(\chi_{3800}(1, \cdot)\) 3800.2.a.a 1 1
3800.2.a.b 1
3800.2.a.c 1
3800.2.a.d 1
3800.2.a.e 1
3800.2.a.f 1
3800.2.a.g 1
3800.2.a.h 1
3800.2.a.i 1
3800.2.a.j 2
3800.2.a.k 2
3800.2.a.l 2
3800.2.a.m 2
3800.2.a.n 2
3800.2.a.o 2
3800.2.a.p 2
3800.2.a.q 2
3800.2.a.r 3
3800.2.a.s 3
3800.2.a.t 3
3800.2.a.u 3
3800.2.a.v 3
3800.2.a.w 3
3800.2.a.x 3
3800.2.a.y 3
3800.2.a.z 6
3800.2.a.ba 6
3800.2.a.bb 6
3800.2.a.bc 6
3800.2.a.bd 6
3800.2.a.be 6
3800.2.d \(\chi_{3800}(3649, \cdot)\) 3800.2.d.a 2 1
3800.2.d.b 2
3800.2.d.c 2
3800.2.d.d 2
3800.2.d.e 2
3800.2.d.f 2
3800.2.d.g 2
3800.2.d.h 4
3800.2.d.i 4
3800.2.d.j 6
3800.2.d.k 6
3800.2.d.l 6
3800.2.d.m 6
3800.2.d.n 6
3800.2.d.o 6
3800.2.d.p 12
3800.2.d.q 12
3800.2.e \(\chi_{3800}(2051, \cdot)\) n/a 374 1
3800.2.f \(\chi_{3800}(1901, \cdot)\) n/a 342 1
3800.2.g \(\chi_{3800}(3799, \cdot)\) None 0 1
3800.2.j \(\chi_{3800}(151, \cdot)\) None 0 1
3800.2.k \(\chi_{3800}(1749, \cdot)\) n/a 324 1
3800.2.p \(\chi_{3800}(1899, \cdot)\) n/a 356 1
3800.2.q \(\chi_{3800}(201, \cdot)\) n/a 190 2
3800.2.t \(\chi_{3800}(493, \cdot)\) n/a 712 2
3800.2.u \(\chi_{3800}(343, \cdot)\) None 0 2
3800.2.v \(\chi_{3800}(2393, \cdot)\) n/a 180 2
3800.2.w \(\chi_{3800}(2243, \cdot)\) n/a 648 2
3800.2.z \(\chi_{3800}(761, \cdot)\) n/a 544 4
3800.2.ba \(\chi_{3800}(349, \cdot)\) n/a 712 2
3800.2.bb \(\chi_{3800}(1551, \cdot)\) None 0 2
3800.2.bg \(\chi_{3800}(1699, \cdot)\) n/a 712 2
3800.2.bj \(\chi_{3800}(1851, \cdot)\) n/a 748 2
3800.2.bk \(\chi_{3800}(49, \cdot)\) n/a 180 2
3800.2.bl \(\chi_{3800}(1399, \cdot)\) None 0 2
3800.2.bm \(\chi_{3800}(501, \cdot)\) n/a 748 2
3800.2.bp \(\chi_{3800}(1201, \cdot)\) n/a 570 6
3800.2.bs \(\chi_{3800}(229, \cdot)\) n/a 2160 4
3800.2.bt \(\chi_{3800}(911, \cdot)\) None 0 4
3800.2.bu \(\chi_{3800}(379, \cdot)\) n/a 2384 4
3800.2.bx \(\chi_{3800}(531, \cdot)\) n/a 2384 4
3800.2.by \(\chi_{3800}(609, \cdot)\) n/a 536 4
3800.2.cd \(\chi_{3800}(759, \cdot)\) None 0 4
3800.2.ce \(\chi_{3800}(381, \cdot)\) n/a 2160 4
3800.2.cf \(\chi_{3800}(293, \cdot)\) n/a 1424 4
3800.2.cg \(\chi_{3800}(7, \cdot)\) None 0 4
3800.2.cl \(\chi_{3800}(1057, \cdot)\) n/a 360 4
3800.2.cm \(\chi_{3800}(843, \cdot)\) n/a 1424 4
3800.2.cn \(\chi_{3800}(121, \cdot)\) n/a 1200 8
3800.2.co \(\chi_{3800}(299, \cdot)\) n/a 2136 6
3800.2.ct \(\chi_{3800}(101, \cdot)\) n/a 2244 6
3800.2.cu \(\chi_{3800}(599, \cdot)\) None 0 6
3800.2.cx \(\chi_{3800}(1049, \cdot)\) n/a 540 6
3800.2.cy \(\chi_{3800}(51, \cdot)\) n/a 2244 6
3800.2.cz \(\chi_{3800}(751, \cdot)\) None 0 6
3800.2.da \(\chi_{3800}(149, \cdot)\) n/a 2136 6
3800.2.df \(\chi_{3800}(267, \cdot)\) n/a 4320 8
3800.2.dg \(\chi_{3800}(113, \cdot)\) n/a 1200 8
3800.2.dh \(\chi_{3800}(647, \cdot)\) None 0 8
3800.2.di \(\chi_{3800}(37, \cdot)\) n/a 4768 8
3800.2.dl \(\chi_{3800}(729, \cdot)\) n/a 1200 8
3800.2.dm \(\chi_{3800}(331, \cdot)\) n/a 4768 8
3800.2.dr \(\chi_{3800}(581, \cdot)\) n/a 4768 8
3800.2.ds \(\chi_{3800}(559, \cdot)\) None 0 8
3800.2.dv \(\chi_{3800}(31, \cdot)\) None 0 8
3800.2.dw \(\chi_{3800}(429, \cdot)\) n/a 4768 8
3800.2.dx \(\chi_{3800}(179, \cdot)\) n/a 4768 8
3800.2.ec \(\chi_{3800}(193, \cdot)\) n/a 1080 12
3800.2.ed \(\chi_{3800}(43, \cdot)\) n/a 4272 12
3800.2.eg \(\chi_{3800}(357, \cdot)\) n/a 4272 12
3800.2.eh \(\chi_{3800}(207, \cdot)\) None 0 12
3800.2.ei \(\chi_{3800}(81, \cdot)\) n/a 3600 24
3800.2.ej \(\chi_{3800}(83, \cdot)\) n/a 9536 16
3800.2.ek \(\chi_{3800}(217, \cdot)\) n/a 2400 16
3800.2.ep \(\chi_{3800}(87, \cdot)\) None 0 16
3800.2.eq \(\chi_{3800}(373, \cdot)\) n/a 9536 16
3800.2.er \(\chi_{3800}(79, \cdot)\) None 0 24
3800.2.es \(\chi_{3800}(61, \cdot)\) n/a 14304 24
3800.2.ex \(\chi_{3800}(59, \cdot)\) n/a 14304 24
3800.2.fa \(\chi_{3800}(309, \cdot)\) n/a 14304 24
3800.2.fb \(\chi_{3800}(71, \cdot)\) None 0 24
3800.2.fc \(\chi_{3800}(91, \cdot)\) n/a 14304 24
3800.2.fd \(\chi_{3800}(9, \cdot)\) n/a 3600 24
3800.2.fg \(\chi_{3800}(23, \cdot)\) None 0 48
3800.2.fh \(\chi_{3800}(13, \cdot)\) n/a 28608 48
3800.2.fk \(\chi_{3800}(123, \cdot)\) n/a 28608 48
3800.2.fl \(\chi_{3800}(33, \cdot)\) n/a 7200 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3800))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3800)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(380))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(475))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(760))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(950))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1900))\)\(^{\oplus 2}\)