Properties

Label 2850.2
Level 2850
Weight 2
Dimension 49496
Nonzero newspaces 36
Sturm bound 864000
Trace bound 15

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Defining parameters

Level: \( N \) = \( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(864000\)
Trace bound: \(15\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2850))\).

Total New Old
Modular forms 220032 49496 170536
Cusp forms 211969 49496 162473
Eisenstein series 8063 0 8063

Trace form

\( 49496q - 6q^{2} - 14q^{3} - 6q^{4} - 20q^{5} - 14q^{6} - 48q^{7} - 6q^{8} - 6q^{9} + O(q^{10}) \) \( 49496q - 6q^{2} - 14q^{3} - 6q^{4} - 20q^{5} - 14q^{6} - 48q^{7} - 6q^{8} - 6q^{9} - 4q^{10} - 8q^{11} + 12q^{12} - 68q^{13} - 20q^{14} + 8q^{15} - 6q^{16} + 32q^{17} + 46q^{18} - 32q^{19} + 16q^{20} + 22q^{21} + 66q^{22} + 76q^{23} + 26q^{24} + 172q^{25} - 40q^{26} - 29q^{27} + 20q^{28} + 40q^{29} + 40q^{30} - 4q^{31} + 14q^{32} - 14q^{33} + 56q^{34} + 16q^{35} - 6q^{36} + 12q^{37} - 12q^{38} + 54q^{39} + 12q^{40} - 48q^{41} + 16q^{42} + 80q^{43} - 40q^{44} + 140q^{45} + 48q^{46} + 28q^{47} + 27q^{48} + 90q^{49} - 36q^{50} + 141q^{51} - 20q^{52} + 48q^{53} + 40q^{54} + 48q^{55} - 16q^{56} + 110q^{57} - 116q^{58} - 40q^{59} - 64q^{60} - 176q^{61} - 96q^{62} - 102q^{63} - 6q^{64} - 148q^{65} - 24q^{66} - 288q^{67} - 12q^{68} - 306q^{69} - 96q^{70} - 84q^{71} - 29q^{72} - 274q^{73} - 68q^{74} - 328q^{75} + 4q^{76} + 24q^{77} + 16q^{78} + 292q^{79} - 20q^{80} + 466q^{81} + 380q^{82} + 680q^{83} + 242q^{84} + 508q^{85} + 464q^{86} + 848q^{87} - 40q^{88} + 712q^{89} + 252q^{90} + 960q^{91} + 456q^{92} + 1042q^{93} + 848q^{94} + 416q^{95} + 18q^{96} + 696q^{97} + 858q^{98} + 1031q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2850))\)

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
2850.2.a \(\chi_{2850}(1, \cdot)\) 2850.2.a.a 1 1
2850.2.a.b 1
2850.2.a.c 1
2850.2.a.d 1
2850.2.a.e 1
2850.2.a.f 1
2850.2.a.g 1
2850.2.a.h 1
2850.2.a.i 1
2850.2.a.j 1
2850.2.a.k 1
2850.2.a.l 1
2850.2.a.m 1
2850.2.a.n 1
2850.2.a.o 1
2850.2.a.p 1
2850.2.a.q 1
2850.2.a.r 1
2850.2.a.s 1
2850.2.a.t 1
2850.2.a.u 1
2850.2.a.v 1
2850.2.a.w 1
2850.2.a.x 1
2850.2.a.y 1
2850.2.a.z 1
2850.2.a.ba 1
2850.2.a.bb 1
2850.2.a.bc 2
2850.2.a.bd 2
2850.2.a.be 2
2850.2.a.bf 2
2850.2.a.bg 2
2850.2.a.bh 2
2850.2.a.bi 2
2850.2.a.bj 2
2850.2.a.bk 3
2850.2.a.bl 3
2850.2.a.bm 3
2850.2.a.bn 3
2850.2.c \(\chi_{2850}(2849, \cdot)\) n/a 120 1
2850.2.d \(\chi_{2850}(799, \cdot)\) 2850.2.d.a 2 1
2850.2.d.b 2
2850.2.d.c 2
2850.2.d.d 2
2850.2.d.e 2
2850.2.d.f 2
2850.2.d.g 2
2850.2.d.h 2
2850.2.d.i 2
2850.2.d.j 2
2850.2.d.k 2
2850.2.d.l 2
2850.2.d.m 2
2850.2.d.n 2
2850.2.d.o 2
2850.2.d.p 2
2850.2.d.q 2
2850.2.d.r 2
2850.2.d.s 2
2850.2.d.t 2
2850.2.d.u 4
2850.2.d.v 4
2850.2.d.w 4
2850.2.d.x 4
2850.2.f \(\chi_{2850}(2051, \cdot)\) n/a 128 1
2850.2.i \(\chi_{2850}(2101, \cdot)\) n/a 124 2
2850.2.k \(\chi_{2850}(2243, \cdot)\) n/a 216 2
2850.2.m \(\chi_{2850}(493, \cdot)\) n/a 120 2
2850.2.n \(\chi_{2850}(571, \cdot)\) n/a 368 4
2850.2.o \(\chi_{2850}(449, \cdot)\) n/a 240 2
2850.2.r \(\chi_{2850}(49, \cdot)\) n/a 120 2
2850.2.t \(\chi_{2850}(2501, \cdot)\) n/a 256 2
2850.2.v \(\chi_{2850}(301, \cdot)\) n/a 384 6
2850.2.x \(\chi_{2850}(229, \cdot)\) n/a 352 4
2850.2.y \(\chi_{2850}(569, \cdot)\) n/a 800 4
2850.2.bc \(\chi_{2850}(341, \cdot)\) n/a 800 4
2850.2.bd \(\chi_{2850}(1493, \cdot)\) n/a 480 4
2850.2.bf \(\chi_{2850}(943, \cdot)\) n/a 240 4
2850.2.bh \(\chi_{2850}(121, \cdot)\) n/a 800 8
2850.2.bk \(\chi_{2850}(401, \cdot)\) n/a 756 6
2850.2.bl \(\chi_{2850}(199, \cdot)\) n/a 360 6
2850.2.bo \(\chi_{2850}(299, \cdot)\) n/a 720 6
2850.2.bp \(\chi_{2850}(37, \cdot)\) n/a 800 8
2850.2.br \(\chi_{2850}(77, \cdot)\) n/a 1440 8
2850.2.bt \(\chi_{2850}(619, \cdot)\) n/a 800 8
2850.2.bw \(\chi_{2850}(179, \cdot)\) n/a 1600 8
2850.2.by \(\chi_{2850}(221, \cdot)\) n/a 1600 8
2850.2.cb \(\chi_{2850}(193, \cdot)\) n/a 720 12
2850.2.cc \(\chi_{2850}(443, \cdot)\) n/a 1440 12
2850.2.ce \(\chi_{2850}(61, \cdot)\) n/a 2400 24
2850.2.cg \(\chi_{2850}(103, \cdot)\) n/a 1600 16
2850.2.ci \(\chi_{2850}(83, \cdot)\) n/a 3200 16
2850.2.cj \(\chi_{2850}(41, \cdot)\) n/a 4800 24
2850.2.cm \(\chi_{2850}(29, \cdot)\) n/a 4800 24
2850.2.cp \(\chi_{2850}(139, \cdot)\) n/a 2400 24
2850.2.cr \(\chi_{2850}(17, \cdot)\) n/a 9600 48
2850.2.cs \(\chi_{2850}(13, \cdot)\) n/a 4800 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2850))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2850)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(285))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(475))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(570))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(950))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1425))\)\(^{\oplus 2}\)