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Properties

Label 2750.2
Level 2750
Weight 2
Dimension 67968
Nonzero newspaces 36
Sturm bound 900000
Trace bound 27

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Defining parameters

Level: \( N \) = \( 2750 = 2 \cdot 5^{3} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(900000\)
Trace bound: \(27\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2750))\).

Total New Old
Modular forms 228600 67968 160632
Cusp forms 221401 67968 153433
Eisenstein series 7199 0 7199

Trace form

\( 67968 q - 2 q^{2} - 8 q^{3} - 2 q^{4} - 8 q^{6} - 16 q^{7} - 2 q^{8} - 26 q^{9} + O(q^{10}) \) \( 67968 q - 2 q^{2} - 8 q^{3} - 2 q^{4} - 8 q^{6} - 16 q^{7} - 2 q^{8} - 26 q^{9} - 12 q^{11} - 8 q^{12} - 28 q^{13} - 16 q^{14} - 2 q^{16} + 44 q^{17} + 74 q^{18} + 120 q^{19} + 10 q^{20} + 96 q^{21} + 68 q^{22} + 112 q^{23} + 72 q^{24} + 120 q^{25} + 52 q^{26} + 160 q^{27} + 64 q^{28} + 100 q^{29} + 80 q^{30} + 96 q^{31} + 18 q^{32} + 32 q^{33} + 64 q^{34} + 40 q^{35} - 26 q^{36} - 56 q^{37} - 40 q^{38} + 48 q^{39} - 4 q^{41} - 24 q^{42} + 152 q^{43} + 28 q^{44} + 160 q^{45} + 32 q^{46} + 184 q^{47} - 8 q^{48} + 266 q^{49} + 256 q^{51} + 52 q^{52} + 192 q^{53} + 80 q^{54} + 40 q^{55} - 16 q^{56} + 320 q^{57} + 100 q^{58} + 240 q^{59} + 40 q^{60} + 276 q^{61} + 256 q^{62} + 552 q^{63} - 2 q^{64} + 210 q^{65} + 152 q^{66} + 304 q^{67} + 244 q^{68} + 448 q^{69} + 160 q^{70} + 176 q^{71} - 26 q^{72} + 172 q^{73} + 324 q^{74} + 320 q^{75} + 120 q^{76} + 224 q^{77} + 288 q^{78} + 160 q^{79} + 78 q^{81} + 236 q^{82} + 472 q^{83} + 176 q^{84} + 210 q^{85} + 152 q^{86} + 320 q^{87} - 12 q^{88} + 240 q^{89} + 120 q^{90} + 136 q^{91} + 32 q^{92} + 104 q^{93} - 96 q^{94} + 80 q^{95} - 8 q^{96} + 4 q^{97} - 114 q^{98} + 164 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2750))\)

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
2750.2.a \(\chi_{2750}(1, \cdot)\) 2750.2.a.a 2 1
2750.2.a.b 2
2750.2.a.c 2
2750.2.a.d 2
2750.2.a.e 2
2750.2.a.f 2
2750.2.a.g 4
2750.2.a.h 4
2750.2.a.i 4
2750.2.a.j 4
2750.2.a.k 4
2750.2.a.l 4
2750.2.a.m 4
2750.2.a.n 4
2750.2.a.o 4
2750.2.a.p 4
2750.2.a.q 6
2750.2.a.r 6
2750.2.a.s 8
2750.2.a.t 8
2750.2.b \(\chi_{2750}(749, \cdot)\) 2750.2.b.a 4 1
2750.2.b.b 4
2750.2.b.c 4
2750.2.b.d 8
2750.2.b.e 8
2750.2.b.f 8
2750.2.b.g 8
2750.2.b.h 8
2750.2.b.i 12
2750.2.b.j 16
2750.2.f \(\chi_{2750}(307, \cdot)\) n/a 192 2
2750.2.g \(\chi_{2750}(801, \cdot)\) n/a 360 4
2750.2.h \(\chi_{2750}(251, \cdot)\) n/a 384 4
2750.2.i \(\chi_{2750}(201, \cdot)\) n/a 360 4
2750.2.j \(\chi_{2750}(1401, \cdot)\) n/a 360 4
2750.2.k \(\chi_{2750}(551, \cdot)\) n/a 304 4
2750.2.l \(\chi_{2750}(401, \cdot)\) n/a 360 4
2750.2.n \(\chi_{2750}(599, \cdot)\) n/a 360 4
2750.2.t \(\chi_{2750}(199, \cdot)\) n/a 296 4
2750.2.y \(\chi_{2750}(399, \cdot)\) n/a 360 4
2750.2.z \(\chi_{2750}(49, \cdot)\) n/a 360 4
2750.2.ba \(\chi_{2750}(499, \cdot)\) n/a 384 4
2750.2.bb \(\chi_{2750}(1149, \cdot)\) n/a 360 4
2750.2.be \(\chi_{2750}(293, \cdot)\) n/a 720 8
2750.2.bh \(\chi_{2750}(57, \cdot)\) n/a 768 8
2750.2.bi \(\chi_{2750}(43, \cdot)\) n/a 720 8
2750.2.bj \(\chi_{2750}(1107, \cdot)\) n/a 720 8
2750.2.bk \(\chi_{2750}(7, \cdot)\) n/a 720 8
2750.2.bp \(\chi_{2750}(607, \cdot)\) n/a 720 8
2750.2.bq \(\chi_{2750}(81, \cdot)\) n/a 3000 20
2750.2.br \(\chi_{2750}(181, \cdot)\) n/a 3000 20
2750.2.bs \(\chi_{2750}(111, \cdot)\) n/a 2480 20
2750.2.bt \(\chi_{2750}(291, \cdot)\) n/a 3000 20
2750.2.bu \(\chi_{2750}(31, \cdot)\) n/a 3000 20
2750.2.bv \(\chi_{2750}(119, \cdot)\) n/a 3000 20
2750.2.cc \(\chi_{2750}(89, \cdot)\) n/a 2520 20
2750.2.cd \(\chi_{2750}(59, \cdot)\) n/a 3000 20
2750.2.ce \(\chi_{2750}(9, \cdot)\) n/a 3000 20
2750.2.ci \(\chi_{2750}(69, \cdot)\) n/a 3000 20
2750.2.cl \(\chi_{2750}(63, \cdot)\) n/a 6000 40
2750.2.cm \(\chi_{2750}(123, \cdot)\) n/a 6000 40
2750.2.cq \(\chi_{2750}(13, \cdot)\) n/a 6000 40
2750.2.cr \(\chi_{2750}(17, \cdot)\) n/a 6000 40
2750.2.cs \(\chi_{2750}(87, \cdot)\) n/a 6000 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2750))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2750)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(250))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(550))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1375))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2750))\)\(^{\oplus 1}\)