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Properties

Label 1100.6
Level 1100
Weight 6
Dimension 94793
Nonzero newspaces 42
Sturm bound 432000
Trace bound 13

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Defining parameters

Level: \( N \) = \( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 42 \)
Sturm bound: \(432000\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(1100))\).

Total New Old
Modular forms 181400 95533 85867
Cusp forms 178600 94793 83807
Eisenstein series 2800 740 2060

Trace form

\( 94793 q - 53 q^{2} + 16 q^{3} - 45 q^{4} - 90 q^{5} - 805 q^{6} + 639 q^{7} + 931 q^{8} + 682 q^{9} + O(q^{10}) \) \( 94793 q - 53 q^{2} + 16 q^{3} - 45 q^{4} - 90 q^{5} - 805 q^{6} + 639 q^{7} + 931 q^{8} + 682 q^{9} + 1072 q^{10} - 185 q^{11} - 5230 q^{12} - 4109 q^{13} + 2650 q^{14} - 4876 q^{15} + 1455 q^{16} + 8397 q^{17} - 15054 q^{18} + 2827 q^{19} - 2788 q^{20} + 28028 q^{21} + 7635 q^{22} - 23743 q^{23} + 205 q^{24} - 366 q^{25} + 10970 q^{26} + 26008 q^{27} + 360 q^{28} + 44527 q^{29} + 17140 q^{30} + 5928 q^{31} + 70392 q^{32} - 34190 q^{33} + 10790 q^{34} + 15536 q^{35} - 63070 q^{36} - 123702 q^{37} - 206620 q^{38} + 80417 q^{39} + 92952 q^{40} + 93503 q^{41} + 154170 q^{42} + 117190 q^{43} - 11500 q^{44} - 129930 q^{45} - 30270 q^{46} - 315377 q^{47} - 92360 q^{48} - 294731 q^{49} - 194868 q^{50} - 3759 q^{51} + 87574 q^{52} - 15745 q^{53} + 132260 q^{54} + 335800 q^{55} - 282360 q^{56} + 799901 q^{57} - 335708 q^{58} + 233044 q^{59} + 180060 q^{60} - 108789 q^{61} - 365920 q^{62} - 1306756 q^{63} - 457005 q^{64} - 969930 q^{65} + 580040 q^{66} - 48161 q^{67} + 1442392 q^{68} + 501951 q^{69} + 728420 q^{70} + 97844 q^{71} + 838977 q^{72} + 954531 q^{73} - 329190 q^{74} + 996476 q^{75} - 1174160 q^{76} - 421765 q^{77} - 2216280 q^{78} - 997919 q^{79} - 935708 q^{80} - 2468773 q^{81} + 20129 q^{82} - 858193 q^{83} - 87030 q^{84} + 149546 q^{85} + 978475 q^{86} + 942026 q^{87} - 365455 q^{88} + 3076743 q^{89} - 1453008 q^{90} - 295403 q^{91} - 445760 q^{92} + 1226156 q^{93} + 1903640 q^{94} + 401448 q^{95} + 3687880 q^{96} - 1086202 q^{97} + 3443536 q^{98} + 2057050 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(1100))\)

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
1100.6.a \(\chi_{1100}(1, \cdot)\) 1100.6.a.a 1 1
1100.6.a.b 2
1100.6.a.c 2
1100.6.a.d 3
1100.6.a.e 4
1100.6.a.f 4
1100.6.a.g 5
1100.6.a.h 8
1100.6.a.i 8
1100.6.a.j 8
1100.6.a.k 8
1100.6.a.l 12
1100.6.a.m 14
1100.6.b \(\chi_{1100}(749, \cdot)\) 1100.6.b.a 2 1
1100.6.b.b 4
1100.6.b.c 4
1100.6.b.d 6
1100.6.b.e 8
1100.6.b.f 8
1100.6.b.g 10
1100.6.b.h 16
1100.6.b.i 16
1100.6.d \(\chi_{1100}(351, \cdot)\) n/a 564 1
1100.6.g \(\chi_{1100}(1099, \cdot)\) n/a 536 1
1100.6.k \(\chi_{1100}(593, \cdot)\) n/a 180 2
1100.6.l \(\chi_{1100}(243, \cdot)\) n/a 900 2
1100.6.m \(\chi_{1100}(361, \cdot)\) n/a 600 4
1100.6.n \(\chi_{1100}(201, \cdot)\) n/a 380 4
1100.6.o \(\chi_{1100}(581, \cdot)\) n/a 600 4
1100.6.p \(\chi_{1100}(81, \cdot)\) n/a 600 4
1100.6.q \(\chi_{1100}(221, \cdot)\) n/a 496 4
1100.6.r \(\chi_{1100}(181, \cdot)\) n/a 600 4
1100.6.s \(\chi_{1100}(491, \cdot)\) n/a 3584 4
1100.6.u \(\chi_{1100}(229, \cdot)\) n/a 600 4
1100.6.w \(\chi_{1100}(219, \cdot)\) n/a 3584 4
1100.6.bc \(\chi_{1100}(299, \cdot)\) n/a 2144 4
1100.6.bd \(\chi_{1100}(19, \cdot)\) n/a 3584 4
1100.6.be \(\chi_{1100}(139, \cdot)\) n/a 3584 4
1100.6.bf \(\chi_{1100}(39, \cdot)\) n/a 3584 4
1100.6.bm \(\chi_{1100}(89, \cdot)\) n/a 504 4
1100.6.br \(\chi_{1100}(371, \cdot)\) n/a 3584 4
1100.6.bs \(\chi_{1100}(51, \cdot)\) n/a 2256 4
1100.6.bt \(\chi_{1100}(211, \cdot)\) n/a 3584 4
1100.6.bu \(\chi_{1100}(171, \cdot)\) n/a 3584 4
1100.6.bz \(\chi_{1100}(9, \cdot)\) n/a 600 4
1100.6.ca \(\chi_{1100}(69, \cdot)\) n/a 600 4
1100.6.cb \(\chi_{1100}(49, \cdot)\) n/a 360 4
1100.6.cc \(\chi_{1100}(389, \cdot)\) n/a 600 4
1100.6.ce \(\chi_{1100}(131, \cdot)\) n/a 3584 4
1100.6.ch \(\chi_{1100}(79, \cdot)\) n/a 3584 4
1100.6.ci \(\chi_{1100}(223, \cdot)\) n/a 7168 8
1100.6.cj \(\chi_{1100}(17, \cdot)\) n/a 1200 8
1100.6.co \(\chi_{1100}(57, \cdot)\) n/a 720 8
1100.6.cp \(\chi_{1100}(103, \cdot)\) n/a 7168 8
1100.6.cq \(\chi_{1100}(23, \cdot)\) n/a 6000 8
1100.6.cr \(\chi_{1100}(3, \cdot)\) n/a 7168 8
1100.6.cs \(\chi_{1100}(153, \cdot)\) n/a 1200 8
1100.6.ct \(\chi_{1100}(13, \cdot)\) n/a 1200 8
1100.6.cu \(\chi_{1100}(217, \cdot)\) n/a 1200 8
1100.6.cv \(\chi_{1100}(207, \cdot)\) n/a 4288 8
1100.6.de \(\chi_{1100}(203, \cdot)\) n/a 7168 8
1100.6.df \(\chi_{1100}(73, \cdot)\) n/a 1200 8

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(1100))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(1100)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(550))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(1100))\)\(^{\oplus 1}\)