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Properties

Label 2548.2
Level 2548
Weight 2
Dimension 108209
Nonzero newspaces 60
Sturm bound 790272
Trace bound 11

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Defining parameters

Level: \( N \) = \( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(790272\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2548))\).

Total New Old
Modular forms 201168 110345 90823
Cusp forms 193969 108209 85760
Eisenstein series 7199 2136 5063

Trace form

\( 108209 q - 156 q^{2} - 4 q^{3} - 156 q^{4} - 324 q^{5} - 144 q^{6} - 8 q^{7} - 264 q^{8} - 312 q^{9} + O(q^{10}) \) \( 108209 q - 156 q^{2} - 4 q^{3} - 156 q^{4} - 324 q^{5} - 144 q^{6} - 8 q^{7} - 264 q^{8} - 312 q^{9} - 120 q^{10} + 6 q^{11} - 90 q^{12} - 334 q^{13} - 372 q^{14} + 12 q^{15} - 108 q^{16} - 327 q^{17} - 114 q^{18} + 8 q^{19} - 120 q^{20} - 338 q^{21} - 294 q^{22} - 144 q^{24} - 253 q^{25} - 159 q^{26} - 4 q^{27} - 228 q^{28} - 501 q^{29} - 120 q^{30} + 26 q^{31} - 126 q^{32} - 246 q^{33} - 120 q^{34} + 30 q^{35} - 216 q^{36} - 215 q^{37} - 66 q^{38} + 25 q^{39} - 306 q^{40} - 147 q^{41} - 150 q^{42} + 54 q^{43} - 102 q^{44} - 39 q^{45} - 156 q^{46} + 114 q^{47} - 234 q^{48} - 212 q^{49} - 492 q^{50} + 156 q^{51} - 219 q^{52} - 636 q^{53} - 258 q^{54} + 144 q^{55} - 156 q^{56} - 526 q^{57} - 216 q^{58} + 42 q^{59} - 222 q^{60} - 225 q^{61} - 156 q^{62} + 36 q^{63} - 210 q^{64} - 273 q^{65} - 318 q^{66} + 32 q^{67} - 66 q^{68} - 270 q^{69} - 162 q^{70} + 36 q^{71} - 126 q^{72} - 112 q^{73} - 108 q^{74} + 168 q^{75} - 84 q^{76} - 198 q^{77} - 237 q^{78} + 328 q^{79} - 252 q^{80} + 42 q^{81} - 246 q^{82} + 186 q^{83} - 636 q^{84} - 111 q^{85} - 456 q^{86} + 132 q^{87} - 492 q^{88} - 12 q^{89} - 1008 q^{90} + 64 q^{91} - 876 q^{92} - 442 q^{93} - 654 q^{94} - 36 q^{95} - 1044 q^{96} - 244 q^{97} - 792 q^{98} + 90 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2548))\)

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
2548.2.a \(\chi_{2548}(1, \cdot)\) 2548.2.a.a 1 1
2548.2.a.b 1
2548.2.a.c 1
2548.2.a.d 1
2548.2.a.e 1
2548.2.a.f 1
2548.2.a.g 1
2548.2.a.h 1
2548.2.a.i 1
2548.2.a.j 1
2548.2.a.k 1
2548.2.a.l 2
2548.2.a.m 2
2548.2.a.n 3
2548.2.a.o 3
2548.2.a.p 4
2548.2.a.q 4
2548.2.a.r 6
2548.2.a.s 6
2548.2.f \(\chi_{2548}(391, \cdot)\) n/a 240 1
2548.2.g \(\chi_{2548}(2157, \cdot)\) 2548.2.g.a 4 1
2548.2.g.b 4
2548.2.g.c 4
2548.2.g.d 4
2548.2.g.e 6
2548.2.g.f 6
2548.2.g.g 8
2548.2.g.h 12
2548.2.h \(\chi_{2548}(2547, \cdot)\) n/a 272 1
2548.2.i \(\chi_{2548}(165, \cdot)\) 2548.2.i.a 2 2
2548.2.i.b 2
2548.2.i.c 2
2548.2.i.d 2
2548.2.i.e 2
2548.2.i.f 2
2548.2.i.g 2
2548.2.i.h 2
2548.2.i.i 4
2548.2.i.j 4
2548.2.i.k 4
2548.2.i.l 4
2548.2.i.m 12
2548.2.i.n 18
2548.2.i.o 32
2548.2.j \(\chi_{2548}(1145, \cdot)\) 2548.2.j.a 2 2
2548.2.j.b 2
2548.2.j.c 2
2548.2.j.d 2
2548.2.j.e 2
2548.2.j.f 2
2548.2.j.g 2
2548.2.j.h 2
2548.2.j.i 2
2548.2.j.j 2
2548.2.j.k 4
2548.2.j.l 4
2548.2.j.m 4
2548.2.j.n 4
2548.2.j.o 6
2548.2.j.p 6
2548.2.j.q 8
2548.2.j.r 12
2548.2.j.s 12
2548.2.k \(\chi_{2548}(393, \cdot)\) 2548.2.k.a 2 2
2548.2.k.b 2
2548.2.k.c 2
2548.2.k.d 2
2548.2.k.e 4
2548.2.k.f 4
2548.2.k.g 12
2548.2.k.h 18
2548.2.k.i 18
2548.2.k.j 32
2548.2.l \(\chi_{2548}(373, \cdot)\) 2548.2.l.a 2 2
2548.2.l.b 2
2548.2.l.c 2
2548.2.l.d 2
2548.2.l.e 2
2548.2.l.f 2
2548.2.l.g 2
2548.2.l.h 2
2548.2.l.i 4
2548.2.l.j 4
2548.2.l.k 4
2548.2.l.l 4
2548.2.l.m 12
2548.2.l.n 18
2548.2.l.o 32
2548.2.m \(\chi_{2548}(99, \cdot)\) n/a 554 2
2548.2.n \(\chi_{2548}(489, \cdot)\) 2548.2.n.a 40 2
2548.2.n.b 56
2548.2.u \(\chi_{2548}(589, \cdot)\) 2548.2.u.a 2 2
2548.2.u.b 16
2548.2.u.c 16
2548.2.u.d 18
2548.2.u.e 18
2548.2.u.f 24
2548.2.v \(\chi_{2548}(783, \cdot)\) n/a 544 2
2548.2.w \(\chi_{2548}(803, \cdot)\) n/a 544 2
2548.2.x \(\chi_{2548}(1195, \cdot)\) n/a 544 2
2548.2.y \(\chi_{2548}(753, \cdot)\) 2548.2.y.a 8 2
2548.2.y.b 8
2548.2.y.c 8
2548.2.y.d 12
2548.2.y.e 16
2548.2.y.f 16
2548.2.y.g 24
2548.2.z \(\chi_{2548}(1587, \cdot)\) n/a 480 2
2548.2.ba \(\chi_{2548}(815, \cdot)\) n/a 544 2
2548.2.bb \(\chi_{2548}(569, \cdot)\) 2548.2.bb.a 2 2
2548.2.bb.b 2
2548.2.bb.c 16
2548.2.bb.d 16
2548.2.bb.e 16
2548.2.bb.f 18
2548.2.bb.g 24
2548.2.bc \(\chi_{2548}(979, \cdot)\) n/a 544 2
2548.2.bp \(\chi_{2548}(1011, \cdot)\) n/a 544 2
2548.2.bq \(\chi_{2548}(361, \cdot)\) 2548.2.bq.a 2 2
2548.2.bq.b 2
2548.2.bq.c 16
2548.2.bq.d 16
2548.2.bq.e 16
2548.2.bq.f 18
2548.2.bq.g 24
2548.2.br \(\chi_{2548}(607, \cdot)\) n/a 544 2
2548.2.bs \(\chi_{2548}(365, \cdot)\) n/a 336 6
2548.2.bt \(\chi_{2548}(717, \cdot)\) n/a 188 4
2548.2.bu \(\chi_{2548}(67, \cdot)\) n/a 1088 4
2548.2.cb \(\chi_{2548}(275, \cdot)\) n/a 1088 4
2548.2.cc \(\chi_{2548}(97, \cdot)\) n/a 184 4
2548.2.cd \(\chi_{2548}(1097, \cdot)\) n/a 184 4
2548.2.ce \(\chi_{2548}(687, \cdot)\) n/a 1108 4
2548.2.cf \(\chi_{2548}(655, \cdot)\) n/a 1088 4
2548.2.cg \(\chi_{2548}(509, \cdot)\) n/a 188 4
2548.2.cj \(\chi_{2548}(363, \cdot)\) n/a 2328 6
2548.2.ck \(\chi_{2548}(337, \cdot)\) n/a 384 6
2548.2.cl \(\chi_{2548}(27, \cdot)\) n/a 2016 6
2548.2.cq \(\chi_{2548}(9, \cdot)\) n/a 780 12
2548.2.cr \(\chi_{2548}(29, \cdot)\) n/a 792 12
2548.2.cs \(\chi_{2548}(53, \cdot)\) n/a 672 12
2548.2.ct \(\chi_{2548}(289, \cdot)\) n/a 780 12
2548.2.cw \(\chi_{2548}(125, \cdot)\) n/a 768 12
2548.2.cx \(\chi_{2548}(239, \cdot)\) n/a 4656 12
2548.2.cy \(\chi_{2548}(3, \cdot)\) n/a 4656 12
2548.2.cz \(\chi_{2548}(121, \cdot)\) n/a 780 12
2548.2.da \(\chi_{2548}(283, \cdot)\) n/a 4656 12
2548.2.dn \(\chi_{2548}(251, \cdot)\) n/a 4656 12
2548.2.do \(\chi_{2548}(205, \cdot)\) n/a 780 12
2548.2.dp \(\chi_{2548}(87, \cdot)\) n/a 4656 12
2548.2.dq \(\chi_{2548}(131, \cdot)\) n/a 4032 12
2548.2.dr \(\chi_{2548}(25, \cdot)\) n/a 792 12
2548.2.ds \(\chi_{2548}(103, \cdot)\) n/a 4656 12
2548.2.dt \(\chi_{2548}(75, \cdot)\) n/a 4656 12
2548.2.du \(\chi_{2548}(55, \cdot)\) n/a 4656 12
2548.2.dv \(\chi_{2548}(225, \cdot)\) n/a 792 12
2548.2.ec \(\chi_{2548}(45, \cdot)\) n/a 1560 24
2548.2.ed \(\chi_{2548}(135, \cdot)\) n/a 9312 24
2548.2.ee \(\chi_{2548}(15, \cdot)\) n/a 9312 24
2548.2.ef \(\chi_{2548}(5, \cdot)\) n/a 1584 24
2548.2.eg \(\chi_{2548}(41, \cdot)\) n/a 1584 24
2548.2.eh \(\chi_{2548}(123, \cdot)\) n/a 9312 24
2548.2.eo \(\chi_{2548}(11, \cdot)\) n/a 9312 24
2548.2.ep \(\chi_{2548}(33, \cdot)\) n/a 1560 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2548))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2548)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(364))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(637))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1274))\)\(^{\oplus 2}\)