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Properties

Label 3850.2
Level 3850
Weight 2
Dimension 125074
Nonzero newspaces 84
Sturm bound 1728000
Trace bound 19

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Defining parameters

Level: \( N \) = \( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 84 \)
Sturm bound: \(1728000\)
Trace bound: \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3850))\).

Total New Old
Modular forms 438720 125074 313646
Cusp forms 425281 125074 300207
Eisenstein series 13439 0 13439

Trace form

\( 125074 q - 4 q^{2} - 20 q^{3} - 8 q^{4} - 20 q^{5} - 38 q^{6} - 42 q^{7} - 4 q^{8} - 120 q^{9} + O(q^{10}) \) \( 125074 q - 4 q^{2} - 20 q^{3} - 8 q^{4} - 20 q^{5} - 38 q^{6} - 42 q^{7} - 4 q^{8} - 120 q^{9} - 20 q^{10} - 56 q^{11} - 40 q^{12} - 96 q^{13} - 38 q^{14} - 80 q^{15} - 8 q^{16} - 80 q^{17} + 14 q^{18} + 6 q^{19} - 56 q^{21} + 44 q^{22} - 24 q^{23} + 42 q^{24} + 188 q^{25} + 44 q^{26} + 190 q^{27} + 94 q^{28} + 104 q^{29} + 224 q^{30} + 108 q^{31} + 6 q^{32} + 66 q^{33} + 156 q^{34} + 104 q^{35} + 102 q^{36} + 36 q^{37} + 16 q^{38} + 188 q^{39} - 20 q^{40} - 72 q^{41} + 214 q^{42} + 292 q^{43} + 142 q^{44} + 444 q^{45} + 232 q^{46} + 392 q^{47} - 20 q^{48} + 160 q^{49} + 60 q^{50} + 342 q^{51} + 204 q^{52} + 224 q^{53} + 328 q^{54} + 304 q^{55} - 28 q^{56} + 510 q^{57} + 368 q^{58} + 434 q^{59} + 160 q^{60} + 700 q^{61} + 360 q^{62} + 732 q^{63} - 8 q^{64} + 524 q^{65} + 416 q^{66} + 724 q^{67} + 300 q^{68} + 768 q^{69} + 120 q^{70} + 160 q^{71} + 4 q^{72} + 316 q^{73} + 256 q^{74} + 432 q^{75} + 76 q^{76} + 224 q^{77} + 240 q^{78} + 288 q^{79} - 20 q^{80} + 114 q^{81} + 130 q^{82} + 390 q^{83} + 84 q^{84} + 156 q^{85} + 138 q^{86} + 300 q^{87} + 52 q^{88} + 332 q^{89} + 172 q^{90} + 292 q^{91} + 68 q^{92} + 528 q^{93} + 12 q^{94} + 304 q^{95} + 68 q^{96} + 378 q^{97} + 370 q^{98} + 576 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3850))\)

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
3850.2.a \(\chi_{3850}(1, \cdot)\) 3850.2.a.a 1 1
3850.2.a.b 1
3850.2.a.c 1
3850.2.a.d 1
3850.2.a.e 1
3850.2.a.f 1
3850.2.a.g 1
3850.2.a.h 1
3850.2.a.i 1
3850.2.a.j 1
3850.2.a.k 1
3850.2.a.l 1
3850.2.a.m 1
3850.2.a.n 1
3850.2.a.o 1
3850.2.a.p 1
3850.2.a.q 1
3850.2.a.r 1
3850.2.a.s 1
3850.2.a.t 1
3850.2.a.u 1
3850.2.a.v 1
3850.2.a.w 1
3850.2.a.x 1
3850.2.a.y 1
3850.2.a.z 1
3850.2.a.ba 1
3850.2.a.bb 1
3850.2.a.bc 2
3850.2.a.bd 2
3850.2.a.be 2
3850.2.a.bf 2
3850.2.a.bg 2
3850.2.a.bh 2
3850.2.a.bi 2
3850.2.a.bj 2
3850.2.a.bk 2
3850.2.a.bl 2
3850.2.a.bm 2
3850.2.a.bn 2
3850.2.a.bo 2
3850.2.a.bp 2
3850.2.a.bq 2
3850.2.a.br 3
3850.2.a.bs 3
3850.2.a.bt 3
3850.2.a.bu 3
3850.2.a.bv 3
3850.2.a.bw 3
3850.2.a.bx 4
3850.2.a.by 4
3850.2.a.bz 5
3850.2.a.ca 5
3850.2.c \(\chi_{3850}(1849, \cdot)\) 3850.2.c.a 2 1
3850.2.c.b 2
3850.2.c.c 2
3850.2.c.d 2
3850.2.c.e 2
3850.2.c.f 2
3850.2.c.g 2
3850.2.c.h 2
3850.2.c.i 2
3850.2.c.j 2
3850.2.c.k 2
3850.2.c.l 2
3850.2.c.m 2
3850.2.c.n 2
3850.2.c.o 2
3850.2.c.p 2
3850.2.c.q 4
3850.2.c.r 4
3850.2.c.s 4
3850.2.c.t 4
3850.2.c.u 4
3850.2.c.v 4
3850.2.c.w 4
3850.2.c.x 4
3850.2.c.y 4
3850.2.c.z 6
3850.2.c.ba 6
3850.2.c.bb 6
3850.2.c.bc 6
3850.2.e \(\chi_{3850}(2001, \cdot)\) n/a 152 1
3850.2.g \(\chi_{3850}(3849, \cdot)\) n/a 144 1
3850.2.i \(\chi_{3850}(1101, \cdot)\) n/a 256 2
3850.2.l \(\chi_{3850}(1343, \cdot)\) n/a 240 2
3850.2.m \(\chi_{3850}(43, \cdot)\) n/a 216 2
3850.2.n \(\chi_{3850}(771, \cdot)\) n/a 608 4
3850.2.o \(\chi_{3850}(841, \cdot)\) n/a 720 4
3850.2.p \(\chi_{3850}(1401, \cdot)\) n/a 456 4
3850.2.q \(\chi_{3850}(71, \cdot)\) n/a 720 4
3850.2.r \(\chi_{3850}(141, \cdot)\) n/a 720 4
3850.2.s \(\chi_{3850}(1961, \cdot)\) n/a 720 4
3850.2.t \(\chi_{3850}(549, \cdot)\) n/a 288 2
3850.2.w \(\chi_{3850}(1299, \cdot)\) n/a 240 2
3850.2.y \(\chi_{3850}(901, \cdot)\) n/a 304 2
3850.2.ba \(\chi_{3850}(1709, \cdot)\) n/a 720 4
3850.2.bc \(\chi_{3850}(321, \cdot)\) n/a 960 4
3850.2.bj \(\chi_{3850}(2239, \cdot)\) n/a 960 4
3850.2.bm \(\chi_{3850}(349, \cdot)\) n/a 576 4
3850.2.bn \(\chi_{3850}(1119, \cdot)\) n/a 960 4
3850.2.bo \(\chi_{3850}(769, \cdot)\) n/a 960 4
3850.2.bs \(\chi_{3850}(139, \cdot)\) n/a 960 4
3850.2.bu \(\chi_{3850}(391, \cdot)\) n/a 960 4
3850.2.bv \(\chi_{3850}(461, \cdot)\) n/a 960 4
3850.2.bw \(\chi_{3850}(601, \cdot)\) n/a 608 4
3850.2.ca \(\chi_{3850}(41, \cdot)\) n/a 960 4
3850.2.cb \(\chi_{3850}(1091, \cdot)\) n/a 960 4
3850.2.cd \(\chi_{3850}(169, \cdot)\) n/a 720 4
3850.2.cg \(\chi_{3850}(449, \cdot)\) n/a 432 4
3850.2.ch \(\chi_{3850}(309, \cdot)\) n/a 592 4
3850.2.ci \(\chi_{3850}(1989, \cdot)\) n/a 720 4
3850.2.cm \(\chi_{3850}(379, \cdot)\) n/a 720 4
3850.2.cn \(\chi_{3850}(629, \cdot)\) n/a 960 4
3850.2.cq \(\chi_{3850}(243, \cdot)\) n/a 480 4
3850.2.cr \(\chi_{3850}(1143, \cdot)\) n/a 576 4
3850.2.cu \(\chi_{3850}(191, \cdot)\) n/a 1920 8
3850.2.cv \(\chi_{3850}(81, \cdot)\) n/a 1920 8
3850.2.cw \(\chi_{3850}(641, \cdot)\) n/a 1920 8
3850.2.cx \(\chi_{3850}(401, \cdot)\) n/a 1216 8
3850.2.cy \(\chi_{3850}(291, \cdot)\) n/a 1920 8
3850.2.cz \(\chi_{3850}(221, \cdot)\) n/a 1600 8
3850.2.da \(\chi_{3850}(337, \cdot)\) n/a 1440 8
3850.2.db \(\chi_{3850}(97, \cdot)\) n/a 1920 8
3850.2.dg \(\chi_{3850}(197, \cdot)\) n/a 1440 8
3850.2.dh \(\chi_{3850}(127, \cdot)\) n/a 1440 8
3850.2.di \(\chi_{3850}(57, \cdot)\) n/a 864 8
3850.2.dj \(\chi_{3850}(673, \cdot)\) n/a 1440 8
3850.2.dk \(\chi_{3850}(1203, \cdot)\) n/a 1920 8
3850.2.dl \(\chi_{3850}(643, \cdot)\) n/a 1152 8
3850.2.dm \(\chi_{3850}(27, \cdot)\) n/a 1920 8
3850.2.dn \(\chi_{3850}(573, \cdot)\) n/a 1600 8
3850.2.dw \(\chi_{3850}(797, \cdot)\) n/a 1920 8
3850.2.dx \(\chi_{3850}(897, \cdot)\) n/a 1440 8
3850.2.dz \(\chi_{3850}(369, \cdot)\) n/a 1920 8
3850.2.ec \(\chi_{3850}(61, \cdot)\) n/a 1920 8
3850.2.ed \(\chi_{3850}(171, \cdot)\) n/a 1920 8
3850.2.eh \(\chi_{3850}(101, \cdot)\) n/a 1216 8
3850.2.ei \(\chi_{3850}(131, \cdot)\) n/a 1920 8
3850.2.ej \(\chi_{3850}(271, \cdot)\) n/a 1920 8
3850.2.el \(\chi_{3850}(389, \cdot)\) n/a 1920 8
3850.2.ep \(\chi_{3850}(709, \cdot)\) n/a 1920 8
3850.2.eq \(\chi_{3850}(529, \cdot)\) n/a 1600 8
3850.2.er \(\chi_{3850}(499, \cdot)\) n/a 1152 8
3850.2.eu \(\chi_{3850}(9, \cdot)\) n/a 1920 8
3850.2.fa \(\chi_{3850}(479, \cdot)\) n/a 1920 8
3850.2.fe \(\chi_{3850}(439, \cdot)\) n/a 1920 8
3850.2.ff \(\chi_{3850}(19, \cdot)\) n/a 1920 8
3850.2.fg \(\chi_{3850}(299, \cdot)\) n/a 1152 8
3850.2.fj \(\chi_{3850}(129, \cdot)\) n/a 1920 8
3850.2.fl \(\chi_{3850}(289, \cdot)\) n/a 1920 8
3850.2.fn \(\chi_{3850}(831, \cdot)\) n/a 1920 8
3850.2.fo \(\chi_{3850}(383, \cdot)\) n/a 3840 16
3850.2.fp \(\chi_{3850}(233, \cdot)\) n/a 3840 16
3850.2.fy \(\chi_{3850}(123, \cdot)\) n/a 3840 16
3850.2.fz \(\chi_{3850}(107, \cdot)\) n/a 2304 16
3850.2.ga \(\chi_{3850}(387, \cdot)\) n/a 3840 16
3850.2.gb \(\chi_{3850}(263, \cdot)\) n/a 3840 16
3850.2.gc \(\chi_{3850}(353, \cdot)\) n/a 3200 16
3850.2.gd \(\chi_{3850}(3, \cdot)\) n/a 3840 16
3850.2.ge \(\chi_{3850}(157, \cdot)\) n/a 2304 16
3850.2.gf \(\chi_{3850}(103, \cdot)\) n/a 3840 16
3850.2.gk \(\chi_{3850}(513, \cdot)\) n/a 3840 16
3850.2.gl \(\chi_{3850}(213, \cdot)\) n/a 3840 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3850))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3850)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(350))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(385))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(550))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(770))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1925))\)\(^{\oplus 2}\)