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Properties

Label 837.2
Level 837
Weight 2
Dimension 19974
Nonzero newspaces 32
Newform subspaces 74
Sturm bound 103680
Trace bound 8

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Defining parameters

Level: \( N \) = \( 837 = 3^{3} \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Newform subspaces: \( 74 \)
Sturm bound: \(103680\)
Trace bound: \(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(837))\).

Total New Old
Modular forms 26820 20902 5918
Cusp forms 25021 19974 5047
Eisenstein series 1799 928 871

Trace form

\( 19974 q - 108 q^{2} - 168 q^{3} - 194 q^{4} - 114 q^{5} - 180 q^{6} - 196 q^{7} - 132 q^{8} - 180 q^{9} + O(q^{10}) \) \( 19974 q - 108 q^{2} - 168 q^{3} - 194 q^{4} - 114 q^{5} - 180 q^{6} - 196 q^{7} - 132 q^{8} - 180 q^{9} - 204 q^{10} - 126 q^{11} - 204 q^{12} - 208 q^{13} - 150 q^{14} - 198 q^{15} - 218 q^{16} - 138 q^{17} - 198 q^{18} - 190 q^{19} - 114 q^{20} - 156 q^{21} - 216 q^{22} - 96 q^{23} - 144 q^{24} - 206 q^{25} - 60 q^{26} - 162 q^{27} - 460 q^{28} - 108 q^{29} - 162 q^{30} - 209 q^{31} - 240 q^{32} - 180 q^{33} - 228 q^{34} - 144 q^{35} - 216 q^{36} - 226 q^{37} - 204 q^{38} - 246 q^{39} - 252 q^{40} - 150 q^{41} - 216 q^{42} - 232 q^{43} - 126 q^{44} - 162 q^{45} - 204 q^{46} - 90 q^{47} - 150 q^{48} - 222 q^{49} - 54 q^{50} - 144 q^{51} - 208 q^{52} - 84 q^{53} - 72 q^{54} - 456 q^{55} - 54 q^{56} - 174 q^{57} - 252 q^{58} - 96 q^{59} - 180 q^{60} - 232 q^{61} - 108 q^{62} - 378 q^{63} - 218 q^{64} - 126 q^{65} - 162 q^{66} - 190 q^{67} - 138 q^{68} - 198 q^{69} - 180 q^{70} - 174 q^{71} - 216 q^{72} - 208 q^{73} - 186 q^{74} - 258 q^{75} - 242 q^{76} - 240 q^{77} - 216 q^{78} - 230 q^{79} - 504 q^{80} - 252 q^{81} - 576 q^{82} - 408 q^{83} - 192 q^{84} - 276 q^{85} - 462 q^{86} - 198 q^{87} - 510 q^{88} - 288 q^{89} - 216 q^{90} - 342 q^{91} - 432 q^{92} - 141 q^{93} - 510 q^{94} - 294 q^{95} - 180 q^{96} - 308 q^{97} - 390 q^{98} - 126 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(837))\)

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
837.2.a \(\chi_{837}(1, \cdot)\) 837.2.a.a 2 1
837.2.a.b 2
837.2.a.c 2
837.2.a.d 2
837.2.a.e 2
837.2.a.f 3
837.2.a.g 3
837.2.a.h 4
837.2.a.i 4
837.2.a.j 5
837.2.a.k 5
837.2.a.l 6
837.2.c \(\chi_{837}(836, \cdot)\) 837.2.c.a 2 1
837.2.c.b 2
837.2.c.c 2
837.2.c.d 16
837.2.c.e 20
837.2.e \(\chi_{837}(118, \cdot)\) 837.2.e.a 60 2
837.2.f \(\chi_{837}(280, \cdot)\) 837.2.f.a 30 2
837.2.f.b 30
837.2.g \(\chi_{837}(253, \cdot)\) 837.2.g.a 60 2
837.2.h \(\chi_{837}(676, \cdot)\) 837.2.h.a 2 2
837.2.h.b 16
837.2.h.c 22
837.2.h.d 22
837.2.h.e 24
837.2.i \(\chi_{837}(109, \cdot)\) 837.2.i.a 4 4
837.2.i.b 4
837.2.i.c 8
837.2.i.d 16
837.2.i.e 24
837.2.i.f 36
837.2.i.g 36
837.2.i.h 40
837.2.j \(\chi_{837}(26, \cdot)\) 837.2.j.a 2 2
837.2.j.b 2
837.2.j.c 2
837.2.j.d 16
837.2.j.e 20
837.2.j.f 44
837.2.o \(\chi_{837}(440, \cdot)\) 837.2.o.a 60 2
837.2.r \(\chi_{837}(305, \cdot)\) 837.2.r.a 60 2
837.2.s \(\chi_{837}(278, \cdot)\) 837.2.s.a 60 2
837.2.v \(\chi_{837}(94, \cdot)\) 837.2.v.a 270 6
837.2.v.b 270
837.2.w \(\chi_{837}(160, \cdot)\) 837.2.w.a 564 6
837.2.x \(\chi_{837}(25, \cdot)\) 837.2.x.a 564 6
837.2.z \(\chi_{837}(215, \cdot)\) 837.2.z.a 8 4
837.2.z.b 80
837.2.z.c 80
837.2.bb \(\chi_{837}(28, \cdot)\) 837.2.bb.a 8 8
837.2.bb.b 64
837.2.bb.c 88
837.2.bb.d 88
837.2.bb.e 96
837.2.bc \(\chi_{837}(64, \cdot)\) 837.2.bc.a 240 8
837.2.bd \(\chi_{837}(235, \cdot)\) 837.2.bd.a 240 8
837.2.be \(\chi_{837}(10, \cdot)\) 837.2.be.a 240 8
837.2.bj \(\chi_{837}(92, \cdot)\) 837.2.bj.a 564 6
837.2.bl \(\chi_{837}(68, \cdot)\) 837.2.bl.a 564 6
837.2.bm \(\chi_{837}(212, \cdot)\) 837.2.bm.a 564 6
837.2.bq \(\chi_{837}(44, \cdot)\) 837.2.bq.a 240 8
837.2.bs \(\chi_{837}(89, \cdot)\) 837.2.bs.a 240 8
837.2.bt \(\chi_{837}(17, \cdot)\) 837.2.bt.a 240 8
837.2.bz \(\chi_{837}(53, \cdot)\) 837.2.bz.a 8 8
837.2.bz.b 80
837.2.bz.c 80
837.2.bz.d 176
837.2.ca \(\chi_{837}(7, \cdot)\) 837.2.ca.a 2256 24
837.2.cb \(\chi_{837}(76, \cdot)\) 837.2.cb.a 2256 24
837.2.cc \(\chi_{837}(4, \cdot)\) 837.2.cc.a 2256 24
837.2.ce \(\chi_{837}(65, \cdot)\) 837.2.ce.a 2256 24
837.2.cf \(\chi_{837}(11, \cdot)\) 837.2.cf.a 2256 24
837.2.ch \(\chi_{837}(23, \cdot)\) 837.2.ch.a 2256 24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(837))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(837)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(279))\)\(^{\oplus 2}\)