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Properties

Label 1143.2
Level 1143
Weight 2
Dimension 37737
Nonzero newspaces 32
Sturm bound 193536
Trace bound 6

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Defining parameters

Level: \( N \) = \( 1143 = 3^{2} \cdot 127 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(193536\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1143))\).

Total New Old
Modular forms 49392 38861 10531
Cusp forms 47377 37737 9640
Eisenstein series 2015 1124 891

Trace form

\( 37737 q - 189 q^{2} - 252 q^{3} - 189 q^{4} - 189 q^{5} - 252 q^{6} - 189 q^{7} - 189 q^{8} - 252 q^{9} + O(q^{10}) \) \( 37737 q - 189 q^{2} - 252 q^{3} - 189 q^{4} - 189 q^{5} - 252 q^{6} - 189 q^{7} - 189 q^{8} - 252 q^{9} - 567 q^{10} - 189 q^{11} - 252 q^{12} - 189 q^{13} - 189 q^{14} - 252 q^{15} - 189 q^{16} - 189 q^{17} - 252 q^{18} - 567 q^{19} - 189 q^{20} - 252 q^{21} - 189 q^{22} - 189 q^{23} - 252 q^{24} - 189 q^{25} - 189 q^{26} - 252 q^{27} - 567 q^{28} - 189 q^{29} - 252 q^{30} - 189 q^{31} - 189 q^{32} - 252 q^{33} - 189 q^{34} - 189 q^{35} - 252 q^{36} - 567 q^{37} - 189 q^{38} - 252 q^{39} - 189 q^{40} - 189 q^{41} - 252 q^{42} - 189 q^{43} - 189 q^{44} - 252 q^{45} - 567 q^{46} - 189 q^{47} - 252 q^{48} - 189 q^{49} - 189 q^{50} - 252 q^{51} - 189 q^{52} - 189 q^{53} - 252 q^{54} - 567 q^{55} - 189 q^{56} - 252 q^{57} - 189 q^{58} - 189 q^{59} - 252 q^{60} - 189 q^{61} - 189 q^{62} - 252 q^{63} - 567 q^{64} - 189 q^{65} - 252 q^{66} - 189 q^{67} - 189 q^{68} - 252 q^{69} - 189 q^{70} - 189 q^{71} - 252 q^{72} - 567 q^{73} - 189 q^{74} - 252 q^{75} - 189 q^{76} - 189 q^{77} - 252 q^{78} - 189 q^{79} - 189 q^{80} - 252 q^{81} - 567 q^{82} - 189 q^{83} - 252 q^{84} - 189 q^{85} - 189 q^{86} - 252 q^{87} - 189 q^{88} - 189 q^{89} - 252 q^{90} - 567 q^{91} - 189 q^{92} - 252 q^{93} - 189 q^{94} - 189 q^{95} - 252 q^{96} - 189 q^{97} - 189 q^{98} - 252 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1143))\)

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
1143.2.a \(\chi_{1143}(1, \cdot)\) 1143.2.a.a 1 1
1143.2.a.b 1
1143.2.a.c 1
1143.2.a.d 1
1143.2.a.e 3
1143.2.a.f 4
1143.2.a.g 5
1143.2.a.h 5
1143.2.a.i 7
1143.2.a.j 9
1143.2.a.k 16
1143.2.c \(\chi_{1143}(1142, \cdot)\) 1143.2.c.a 4 1
1143.2.c.b 20
1143.2.c.c 20
1143.2.e \(\chi_{1143}(382, \cdot)\) n/a 252 2
1143.2.f \(\chi_{1143}(742, \cdot)\) n/a 252 2
1143.2.g \(\chi_{1143}(400, \cdot)\) n/a 252 2
1143.2.h \(\chi_{1143}(19, \cdot)\) n/a 106 2
1143.2.j \(\chi_{1143}(782, \cdot)\) 1143.2.j.a 88 2
1143.2.n \(\chi_{1143}(20, \cdot)\) n/a 252 2
1143.2.o \(\chi_{1143}(362, \cdot)\) n/a 252 2
1143.2.p \(\chi_{1143}(380, \cdot)\) n/a 252 2
1143.2.u \(\chi_{1143}(64, \cdot)\) n/a 318 6
1143.2.v \(\chi_{1143}(22, \cdot)\) n/a 756 6
1143.2.w \(\chi_{1143}(103, \cdot)\) n/a 756 6
1143.2.x \(\chi_{1143}(37, \cdot)\) n/a 312 6
1143.2.z \(\chi_{1143}(125, \cdot)\) n/a 264 6
1143.2.bb \(\chi_{1143}(278, \cdot)\) n/a 252 6
1143.2.bg \(\chi_{1143}(59, \cdot)\) n/a 756 6
1143.2.bi \(\chi_{1143}(329, \cdot)\) n/a 756 6
1143.2.bk \(\chi_{1143}(73, \cdot)\) n/a 636 12
1143.2.bl \(\chi_{1143}(61, \cdot)\) n/a 1512 12
1143.2.bm \(\chi_{1143}(25, \cdot)\) n/a 1512 12
1143.2.bn \(\chi_{1143}(4, \cdot)\) n/a 1512 12
1143.2.bs \(\chi_{1143}(95, \cdot)\) n/a 1512 12
1143.2.bt \(\chi_{1143}(5, \cdot)\) n/a 1512 12
1143.2.bu \(\chi_{1143}(77, \cdot)\) n/a 1512 12
1143.2.by \(\chi_{1143}(80, \cdot)\) n/a 528 12
1143.2.ca \(\chi_{1143}(82, \cdot)\) n/a 1872 36
1143.2.cb \(\chi_{1143}(13, \cdot)\) n/a 4536 36
1143.2.cc \(\chi_{1143}(49, \cdot)\) n/a 4536 36
1143.2.ce \(\chi_{1143}(14, \cdot)\) n/a 4536 36
1143.2.cg \(\chi_{1143}(56, \cdot)\) n/a 4536 36
1143.2.cl \(\chi_{1143}(53, \cdot)\) n/a 1512 36

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1143))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1143)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(127))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(381))\)\(^{\oplus 2}\)