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Properties

Label 2169.2
Level 2169
Weight 2
Dimension 136860
Nonzero newspaces 50
Sturm bound 696960
Trace bound 16

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Defining parameters

Level: \( N \) = \( 2169 = 3^{2} \cdot 241 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 50 \)
Sturm bound: \(696960\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2169))\).

Total New Old
Modular forms 176160 139010 37150
Cusp forms 172321 136860 35461
Eisenstein series 3839 2150 1689

Trace form

\( 136860 q - 360 q^{2} - 480 q^{3} - 360 q^{4} - 360 q^{5} - 480 q^{6} - 360 q^{7} - 360 q^{8} - 480 q^{9} + O(q^{10}) \) \( 136860 q - 360 q^{2} - 480 q^{3} - 360 q^{4} - 360 q^{5} - 480 q^{6} - 360 q^{7} - 360 q^{8} - 480 q^{9} - 1080 q^{10} - 360 q^{11} - 480 q^{12} - 360 q^{13} - 360 q^{14} - 480 q^{15} - 360 q^{16} - 360 q^{17} - 480 q^{18} - 1080 q^{19} - 360 q^{20} - 480 q^{21} - 360 q^{22} - 360 q^{23} - 480 q^{24} - 360 q^{25} - 360 q^{26} - 480 q^{27} - 1080 q^{28} - 360 q^{29} - 480 q^{30} - 360 q^{31} - 360 q^{32} - 480 q^{33} - 360 q^{34} - 360 q^{35} - 480 q^{36} - 1080 q^{37} - 360 q^{38} - 480 q^{39} - 360 q^{40} - 360 q^{41} - 480 q^{42} - 360 q^{43} - 360 q^{44} - 480 q^{45} - 1080 q^{46} - 360 q^{47} - 480 q^{48} - 360 q^{49} - 360 q^{50} - 480 q^{51} - 360 q^{52} - 360 q^{53} - 480 q^{54} - 1080 q^{55} - 360 q^{56} - 480 q^{57} - 360 q^{58} - 360 q^{59} - 480 q^{60} - 360 q^{61} - 360 q^{62} - 480 q^{63} - 1080 q^{64} - 360 q^{65} - 480 q^{66} - 360 q^{67} - 360 q^{68} - 480 q^{69} - 360 q^{70} - 360 q^{71} - 480 q^{72} - 1080 q^{73} - 360 q^{74} - 480 q^{75} - 360 q^{76} - 360 q^{77} - 480 q^{78} - 360 q^{79} - 360 q^{80} - 480 q^{81} - 1080 q^{82} - 360 q^{83} - 480 q^{84} - 360 q^{85} - 360 q^{86} - 480 q^{87} - 360 q^{88} - 360 q^{89} - 480 q^{90} - 1080 q^{91} - 360 q^{92} - 480 q^{93} - 360 q^{94} - 360 q^{95} - 480 q^{96} - 360 q^{97} - 360 q^{98} - 480 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2169))\)

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
2169.2.a \(\chi_{2169}(1, \cdot)\) 2169.2.a.a 1 1
2169.2.a.b 1
2169.2.a.c 2
2169.2.a.d 5
2169.2.a.e 7
2169.2.a.f 9
2169.2.a.g 10
2169.2.a.h 12
2169.2.a.i 13
2169.2.a.j 14
2169.2.a.k 26
2169.2.d \(\chi_{2169}(1927, \cdot)\) 2169.2.d.a 4 1
2169.2.d.b 4
2169.2.d.c 16
2169.2.d.d 18
2169.2.d.e 22
2169.2.d.f 36
2169.2.e \(\chi_{2169}(256, \cdot)\) n/a 480 2
2169.2.f \(\chi_{2169}(724, \cdot)\) n/a 480 2
2169.2.g \(\chi_{2169}(1189, \cdot)\) n/a 198 2
2169.2.h \(\chi_{2169}(979, \cdot)\) n/a 480 2
2169.2.i \(\chi_{2169}(64, \cdot)\) n/a 200 2
2169.2.k \(\chi_{2169}(91, \cdot)\) n/a 400 4
2169.2.n \(\chi_{2169}(16, \cdot)\) n/a 480 2
2169.2.o \(\chi_{2169}(481, \cdot)\) n/a 480 2
2169.2.p \(\chi_{2169}(226, \cdot)\) n/a 198 2
2169.2.w \(\chi_{2169}(1462, \cdot)\) n/a 480 2
2169.2.x \(\chi_{2169}(271, \cdot)\) n/a 404 4
2169.2.bb \(\chi_{2169}(154, \cdot)\) n/a 400 4
2169.2.bc \(\chi_{2169}(301, \cdot)\) n/a 960 4
2169.2.bg \(\chi_{2169}(181, \cdot)\) n/a 396 4
2169.2.bh \(\chi_{2169}(4, \cdot)\) n/a 960 4
2169.2.bi \(\chi_{2169}(418, \cdot)\) n/a 960 4
2169.2.bk \(\chi_{2169}(100, \cdot)\) n/a 792 8
2169.2.bl \(\chi_{2169}(205, \cdot)\) n/a 1920 8
2169.2.bm \(\chi_{2169}(265, \cdot)\) n/a 1920 8
2169.2.bn \(\chi_{2169}(94, \cdot)\) n/a 1920 8
2169.2.bo \(\chi_{2169}(44, \cdot)\) n/a 656 8
2169.2.bq \(\chi_{2169}(235, \cdot)\) n/a 800 8
2169.2.bs \(\chi_{2169}(691, \cdot)\) n/a 1920 8
2169.2.bv \(\chi_{2169}(361, \cdot)\) n/a 800 8
2169.2.bx \(\chi_{2169}(121, \cdot)\) n/a 1920 8
2169.2.bz \(\chi_{2169}(211, \cdot)\) n/a 1920 8
2169.2.cc \(\chi_{2169}(10, \cdot)\) n/a 792 8
2169.2.cd \(\chi_{2169}(277, \cdot)\) n/a 1920 8
2169.2.ce \(\chi_{2169}(58, \cdot)\) n/a 1920 8
2169.2.cl \(\chi_{2169}(322, \cdot)\) n/a 1920 8
2169.2.cn \(\chi_{2169}(289, \cdot)\) n/a 1616 16
2169.2.co \(\chi_{2169}(317, \cdot)\) n/a 3840 16
2169.2.cq \(\chi_{2169}(38, \cdot)\) n/a 3840 16
2169.2.cs \(\chi_{2169}(89, \cdot)\) n/a 1280 16
2169.2.cu \(\chi_{2169}(11, \cdot)\) n/a 3840 16
2169.2.cw \(\chi_{2169}(97, \cdot)\) n/a 3840 16
2169.2.da \(\chi_{2169}(25, \cdot)\) n/a 3840 16
2169.2.db \(\chi_{2169}(232, \cdot)\) n/a 3840 16
2169.2.dc \(\chi_{2169}(82, \cdot)\) n/a 1584 16
2169.2.df \(\chi_{2169}(17, \cdot)\) n/a 2624 32
2169.2.dh \(\chi_{2169}(67, \cdot)\) n/a 7680 32
2169.2.di \(\chi_{2169}(61, \cdot)\) n/a 7680 32
2169.2.dk \(\chi_{2169}(49, \cdot)\) n/a 7680 32
2169.2.dm \(\chi_{2169}(244, \cdot)\) n/a 3200 32
2169.2.dp \(\chi_{2169}(74, \cdot)\) n/a 15360 64
2169.2.dr \(\chi_{2169}(14, \cdot)\) n/a 15360 64
2169.2.dt \(\chi_{2169}(35, \cdot)\) n/a 5120 64
2169.2.dv \(\chi_{2169}(23, \cdot)\) n/a 15360 64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2169))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2169)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(241))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(723))\)\(^{\oplus 2}\)