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Properties

Label 2600.2
Level 2600
Weight 2
Dimension 102371
Nonzero newspaces 64
Sturm bound 806400
Trace bound 13

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Defining parameters

Level: \( N \) = \( 2600 = 2^{3} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(806400\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2600))\).

Total New Old
Modular forms 205632 104175 101457
Cusp forms 197569 102371 95198
Eisenstein series 8063 1804 6259

Trace form

\( 102371 q - 132 q^{2} - 132 q^{3} - 132 q^{4} - 2 q^{5} - 212 q^{6} - 148 q^{7} - 132 q^{8} - 284 q^{9} + O(q^{10}) \) \( 102371 q - 132 q^{2} - 132 q^{3} - 132 q^{4} - 2 q^{5} - 212 q^{6} - 148 q^{7} - 132 q^{8} - 284 q^{9} - 160 q^{10} - 228 q^{11} - 84 q^{12} - 4 q^{13} - 240 q^{14} - 144 q^{15} - 148 q^{16} - 259 q^{17} - 20 q^{18} - 80 q^{19} - 120 q^{20} + 8 q^{21} - 52 q^{22} - 128 q^{23} - 20 q^{24} - 330 q^{25} - 420 q^{26} - 276 q^{27} - 148 q^{28} - 39 q^{29} - 152 q^{30} - 192 q^{31} - 212 q^{32} - 288 q^{33} - 260 q^{34} - 136 q^{35} - 304 q^{36} + 31 q^{37} - 212 q^{38} - 68 q^{39} - 432 q^{40} - 383 q^{41} - 140 q^{42} + 92 q^{43} - 120 q^{44} + 158 q^{45} - 188 q^{46} + 96 q^{47} - 52 q^{48} - 102 q^{49} - 120 q^{50} - 144 q^{51} + 12 q^{52} + 150 q^{53} + 88 q^{54} - 16 q^{55} + 120 q^{56} + 4 q^{57} + 156 q^{58} + 80 q^{59} - 72 q^{60} - 3 q^{61} + 168 q^{62} - 44 q^{63} + 84 q^{64} - 325 q^{65} - 320 q^{66} - 208 q^{67} - 36 q^{68} - 4 q^{69} - 152 q^{70} - 324 q^{71} - 284 q^{72} - 176 q^{73} - 196 q^{74} - 304 q^{75} - 508 q^{76} - 112 q^{77} - 264 q^{78} - 616 q^{79} - 200 q^{80} - 396 q^{81} - 420 q^{82} - 536 q^{83} - 648 q^{84} - 146 q^{85} - 436 q^{86} - 524 q^{87} - 656 q^{88} - 206 q^{89} - 760 q^{90} - 296 q^{91} - 808 q^{92} - 204 q^{93} - 724 q^{94} - 416 q^{95} - 604 q^{96} - 372 q^{97} - 736 q^{98} - 340 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2600))\)

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
2600.2.a \(\chi_{2600}(1, \cdot)\) 2600.2.a.a 1 1
2600.2.a.b 1
2600.2.a.c 1
2600.2.a.d 1
2600.2.a.e 1
2600.2.a.f 1
2600.2.a.g 1
2600.2.a.h 1
2600.2.a.i 1
2600.2.a.j 1
2600.2.a.k 1
2600.2.a.l 1
2600.2.a.m 1
2600.2.a.n 2
2600.2.a.o 2
2600.2.a.p 2
2600.2.a.q 2
2600.2.a.r 2
2600.2.a.s 2
2600.2.a.t 2
2600.2.a.u 2
2600.2.a.v 2
2600.2.a.w 2
2600.2.a.x 3
2600.2.a.y 3
2600.2.a.z 4
2600.2.a.ba 4
2600.2.a.bb 5
2600.2.a.bc 5
2600.2.d \(\chi_{2600}(1249, \cdot)\) 2600.2.d.a 2 1
2600.2.d.b 2
2600.2.d.c 2
2600.2.d.d 2
2600.2.d.e 2
2600.2.d.f 2
2600.2.d.g 2
2600.2.d.h 4
2600.2.d.i 4
2600.2.d.j 4
2600.2.d.k 4
2600.2.d.l 4
2600.2.d.m 4
2600.2.d.n 4
2600.2.d.o 4
2600.2.d.p 8
2600.2.e \(\chi_{2600}(701, \cdot)\) n/a 260 1
2600.2.f \(\chi_{2600}(649, \cdot)\) 2600.2.f.a 4 1
2600.2.f.b 4
2600.2.f.c 6
2600.2.f.d 6
2600.2.f.e 8
2600.2.f.f 8
2600.2.f.g 14
2600.2.f.h 14
2600.2.g \(\chi_{2600}(1301, \cdot)\) n/a 228 1
2600.2.j \(\chi_{2600}(2549, \cdot)\) n/a 216 1
2600.2.k \(\chi_{2600}(2001, \cdot)\) 2600.2.k.a 4 1
2600.2.k.b 6
2600.2.k.c 8
2600.2.k.d 14
2600.2.k.e 14
2600.2.k.f 20
2600.2.p \(\chi_{2600}(1949, \cdot)\) n/a 248 1
2600.2.q \(\chi_{2600}(601, \cdot)\) n/a 134 2
2600.2.s \(\chi_{2600}(151, \cdot)\) None 0 2
2600.2.t \(\chi_{2600}(99, \cdot)\) n/a 496 2
2600.2.w \(\chi_{2600}(57, \cdot)\) n/a 126 2
2600.2.y \(\chi_{2600}(1357, \cdot)\) n/a 496 2
2600.2.bb \(\chi_{2600}(807, \cdot)\) None 0 2
2600.2.bc \(\chi_{2600}(1507, \cdot)\) n/a 496 2
2600.2.bd \(\chi_{2600}(207, \cdot)\) None 0 2
2600.2.be \(\chi_{2600}(443, \cdot)\) n/a 432 2
2600.2.bh \(\chi_{2600}(993, \cdot)\) n/a 126 2
2600.2.bj \(\chi_{2600}(957, \cdot)\) n/a 496 2
2600.2.bm \(\chi_{2600}(1451, \cdot)\) n/a 520 2
2600.2.bn \(\chi_{2600}(1399, \cdot)\) None 0 2
2600.2.bp \(\chi_{2600}(521, \cdot)\) n/a 360 4
2600.2.bq \(\chi_{2600}(1349, \cdot)\) n/a 496 2
2600.2.bv \(\chi_{2600}(1401, \cdot)\) n/a 132 2
2600.2.bw \(\chi_{2600}(549, \cdot)\) n/a 496 2
2600.2.bz \(\chi_{2600}(1101, \cdot)\) n/a 520 2
2600.2.ca \(\chi_{2600}(49, \cdot)\) n/a 128 2
2600.2.cb \(\chi_{2600}(101, \cdot)\) n/a 520 2
2600.2.cc \(\chi_{2600}(1049, \cdot)\) n/a 124 2
2600.2.ch \(\chi_{2600}(441, \cdot)\) n/a 424 4
2600.2.ci \(\chi_{2600}(469, \cdot)\) n/a 1440 4
2600.2.cj \(\chi_{2600}(389, \cdot)\) n/a 1664 4
2600.2.cm \(\chi_{2600}(181, \cdot)\) n/a 1664 4
2600.2.cn \(\chi_{2600}(209, \cdot)\) n/a 360 4
2600.2.cs \(\chi_{2600}(261, \cdot)\) n/a 1440 4
2600.2.ct \(\chi_{2600}(129, \cdot)\) n/a 416 4
2600.2.cv \(\chi_{2600}(799, \cdot)\) None 0 4
2600.2.cw \(\chi_{2600}(851, \cdot)\) n/a 1040 4
2600.2.cz \(\chi_{2600}(93, \cdot)\) n/a 992 4
2600.2.db \(\chi_{2600}(657, \cdot)\) n/a 252 4
2600.2.dc \(\chi_{2600}(107, \cdot)\) n/a 992 4
2600.2.dd \(\chi_{2600}(407, \cdot)\) None 0 4
2600.2.di \(\chi_{2600}(43, \cdot)\) n/a 992 4
2600.2.dj \(\chi_{2600}(607, \cdot)\) None 0 4
2600.2.dk \(\chi_{2600}(293, \cdot)\) n/a 992 4
2600.2.dm \(\chi_{2600}(193, \cdot)\) n/a 252 4
2600.2.dp \(\chi_{2600}(899, \cdot)\) n/a 992 4
2600.2.dq \(\chi_{2600}(951, \cdot)\) None 0 4
2600.2.ds \(\chi_{2600}(81, \cdot)\) n/a 832 8
2600.2.du \(\chi_{2600}(239, \cdot)\) None 0 8
2600.2.dv \(\chi_{2600}(291, \cdot)\) n/a 3328 8
2600.2.dx \(\chi_{2600}(317, \cdot)\) n/a 3328 8
2600.2.dz \(\chi_{2600}(73, \cdot)\) n/a 840 8
2600.2.ed \(\chi_{2600}(27, \cdot)\) n/a 2880 8
2600.2.ee \(\chi_{2600}(103, \cdot)\) None 0 8
2600.2.ef \(\chi_{2600}(363, \cdot)\) n/a 3328 8
2600.2.eg \(\chi_{2600}(183, \cdot)\) None 0 8
2600.2.ek \(\chi_{2600}(213, \cdot)\) n/a 3328 8
2600.2.em \(\chi_{2600}(177, \cdot)\) n/a 840 8
2600.2.eo \(\chi_{2600}(619, \cdot)\) n/a 3328 8
2600.2.ep \(\chi_{2600}(31, \cdot)\) None 0 8
2600.2.er \(\chi_{2600}(329, \cdot)\) n/a 832 8
2600.2.es \(\chi_{2600}(61, \cdot)\) n/a 3328 8
2600.2.ex \(\chi_{2600}(9, \cdot)\) n/a 848 8
2600.2.ey \(\chi_{2600}(381, \cdot)\) n/a 3328 8
2600.2.fb \(\chi_{2600}(69, \cdot)\) n/a 3328 8
2600.2.fc \(\chi_{2600}(29, \cdot)\) n/a 3328 8
2600.2.fd \(\chi_{2600}(121, \cdot)\) n/a 848 8
2600.2.fh \(\chi_{2600}(71, \cdot)\) None 0 16
2600.2.fi \(\chi_{2600}(19, \cdot)\) n/a 6656 16
2600.2.fk \(\chi_{2600}(137, \cdot)\) n/a 1680 16
2600.2.fm \(\chi_{2600}(37, \cdot)\) n/a 6656 16
2600.2.fo \(\chi_{2600}(87, \cdot)\) None 0 16
2600.2.fp \(\chi_{2600}(147, \cdot)\) n/a 6656 16
2600.2.fu \(\chi_{2600}(23, \cdot)\) None 0 16
2600.2.fv \(\chi_{2600}(3, \cdot)\) n/a 6656 16
2600.2.fx \(\chi_{2600}(33, \cdot)\) n/a 1680 16
2600.2.fz \(\chi_{2600}(197, \cdot)\) n/a 6656 16
2600.2.gb \(\chi_{2600}(11, \cdot)\) n/a 6656 16
2600.2.gc \(\chi_{2600}(119, \cdot)\) None 0 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2600))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2600)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(260))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(325))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(520))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(650))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1300))\)\(^{\oplus 2}\)