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Properties

Label 187.4
Level 187
Weight 4
Dimension 4084
Nonzero newspaces 10
Newform subspaces 16
Sturm bound 11520
Trace bound 3

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Defining parameters

Level: \( N \) = \( 187 = 11 \cdot 17 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 16 \)
Sturm bound: \(11520\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(187))\).

Total New Old
Modular forms 4480 4356 124
Cusp forms 4160 4084 76
Eisenstein series 320 272 48

Trace form

\( 4084 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} + 46 q^{6} - 34 q^{7} - 134 q^{8} - 214 q^{9} + O(q^{10}) \) \( 4084 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} + 46 q^{6} - 34 q^{7} - 134 q^{8} - 214 q^{9} - 36 q^{10} - 50 q^{11} - 252 q^{12} - 158 q^{13} + 16 q^{14} - 106 q^{15} - 174 q^{16} - 165 q^{17} - 1004 q^{18} - 664 q^{19} - 1148 q^{20} - 692 q^{21} - 1098 q^{22} + 492 q^{23} + 4070 q^{24} + 2522 q^{25} + 2360 q^{26} + 588 q^{27} - 12 q^{28} - 474 q^{29} - 1992 q^{30} - 1002 q^{31} - 2856 q^{32} - 700 q^{33} - 4018 q^{34} - 2242 q^{35} - 3472 q^{36} - 1678 q^{37} - 168 q^{38} + 838 q^{39} + 4848 q^{40} + 1766 q^{41} + 5732 q^{42} + 4284 q^{43} + 4120 q^{44} + 776 q^{45} + 172 q^{46} - 4274 q^{47} - 9512 q^{48} - 5106 q^{49} - 5818 q^{50} - 2854 q^{51} - 3972 q^{52} + 4522 q^{53} + 11732 q^{54} + 5026 q^{55} + 4736 q^{56} + 6932 q^{57} + 496 q^{58} - 956 q^{59} - 632 q^{60} - 1174 q^{61} - 1516 q^{62} - 4360 q^{63} + 2738 q^{64} - 4084 q^{65} - 7848 q^{66} - 6096 q^{67} - 8694 q^{68} - 9456 q^{69} - 2888 q^{70} - 1378 q^{71} - 526 q^{72} + 4446 q^{73} + 2348 q^{74} - 432 q^{75} - 1420 q^{76} + 4606 q^{77} + 6984 q^{78} + 1730 q^{79} + 8584 q^{80} + 8544 q^{81} + 6738 q^{82} + 9888 q^{83} + 18264 q^{84} + 5717 q^{85} + 15054 q^{86} - 4108 q^{87} - 11150 q^{88} - 1816 q^{89} + 2332 q^{90} - 5774 q^{91} - 2028 q^{92} + 886 q^{93} - 7356 q^{94} - 11110 q^{95} - 12648 q^{96} - 2340 q^{97} - 20956 q^{98} - 694 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(187))\)

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
187.4.a \(\chi_{187}(1, \cdot)\) 187.4.a.a 1 1
187.4.a.b 3
187.4.a.c 4
187.4.a.d 10
187.4.a.e 10
187.4.a.f 12
187.4.d \(\chi_{187}(67, \cdot)\) 187.4.d.a 44 1
187.4.e \(\chi_{187}(89, \cdot)\) 187.4.e.a 88 2
187.4.g \(\chi_{187}(69, \cdot)\) 187.4.g.a 88 4
187.4.g.b 104
187.4.h \(\chi_{187}(100, \cdot)\) 187.4.h.a 184 4
187.4.j \(\chi_{187}(16, \cdot)\) 187.4.j.a 208 4
187.4.m \(\chi_{187}(10, \cdot)\) 187.4.m.a 416 8
187.4.p \(\chi_{187}(4, \cdot)\) 187.4.p.a 416 8
187.4.r \(\chi_{187}(9, \cdot)\) 187.4.r.a 832 16
187.4.t \(\chi_{187}(6, \cdot)\) 187.4.t.a 1664 32

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(187))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(187)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 2}\)