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Properties

Label 861.2
Level 861
Weight 2
Dimension 18911
Nonzero newspaces 32
Newform subspaces 65
Sturm bound 107520
Trace bound 8

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Defining parameters

Level: \( N \) = \( 861 = 3 \cdot 7 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Newform subspaces: \( 65 \)
Sturm bound: \(107520\)
Trace bound: \(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(861))\).

Total New Old
Modular forms 27840 19687 8153
Cusp forms 25921 18911 7010
Eisenstein series 1919 776 1143

Trace form

\( 18911 q + 9 q^{2} - 73 q^{3} - 143 q^{4} + 6 q^{5} - 83 q^{6} - 189 q^{7} + 9 q^{8} - 85 q^{9} + O(q^{10}) \) \( 18911 q + 9 q^{2} - 73 q^{3} - 143 q^{4} + 6 q^{5} - 83 q^{6} - 189 q^{7} + 9 q^{8} - 85 q^{9} - 154 q^{10} - 79 q^{12} - 146 q^{13} - 3 q^{14} - 182 q^{15} - 127 q^{16} + 30 q^{17} - 71 q^{18} - 128 q^{19} + 54 q^{20} - 93 q^{21} - 340 q^{22} + 24 q^{23} - 71 q^{24} - 139 q^{25} + 42 q^{26} - 85 q^{27} - 227 q^{28} + 18 q^{29} - 154 q^{30} - 220 q^{31} - 223 q^{32} - 200 q^{33} - 318 q^{34} - 74 q^{35} - 455 q^{36} - 366 q^{37} - 88 q^{38} - 226 q^{39} - 618 q^{40} - 21 q^{41} - 339 q^{42} - 428 q^{43} - 396 q^{44} - 234 q^{45} - 248 q^{46} - 204 q^{47} - 311 q^{48} - 277 q^{49} - 101 q^{50} - 170 q^{51} - 330 q^{52} - 14 q^{53} - 151 q^{54} - 88 q^{55} + 21 q^{56} - 228 q^{57} - 58 q^{58} + 12 q^{59} - 50 q^{60} - 98 q^{61} + 24 q^{62} - 129 q^{63} - 287 q^{64} + 32 q^{65} - 204 q^{66} - 328 q^{67} - 286 q^{68} - 216 q^{69} - 546 q^{70} - 224 q^{71} - 71 q^{72} - 346 q^{73} - 342 q^{74} - 339 q^{75} - 1220 q^{76} - 124 q^{77} - 570 q^{78} - 396 q^{79} - 602 q^{80} - 141 q^{81} - 1015 q^{82} - 236 q^{83} - 367 q^{84} - 996 q^{85} - 656 q^{86} - 198 q^{87} - 804 q^{88} - 170 q^{89} - 290 q^{90} - 518 q^{91} - 312 q^{92} - 160 q^{93} - 760 q^{94} - 188 q^{95} - 423 q^{96} - 394 q^{97} - 203 q^{98} - 188 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(861))\)

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
861.2.a \(\chi_{861}(1, \cdot)\) 861.2.a.a 1 1
861.2.a.b 1
861.2.a.c 1
861.2.a.d 1
861.2.a.e 2
861.2.a.f 2
861.2.a.g 2
861.2.a.h 3
861.2.a.i 4
861.2.a.j 5
861.2.a.k 5
861.2.a.l 5
861.2.a.m 7
861.2.d \(\chi_{861}(83, \cdot)\) 861.2.d.a 4 1
861.2.d.b 4
861.2.d.c 50
861.2.d.d 50
861.2.e \(\chi_{861}(860, \cdot)\) 861.2.e.a 28 1
861.2.e.b 80
861.2.h \(\chi_{861}(778, \cdot)\) 861.2.h.a 18 1
861.2.h.b 22
861.2.i \(\chi_{861}(247, \cdot)\) 861.2.i.a 2 2
861.2.i.b 6
861.2.i.c 6
861.2.i.d 16
861.2.i.e 24
861.2.i.f 26
861.2.i.g 28
861.2.j \(\chi_{861}(337, \cdot)\) 861.2.j.a 40 2
861.2.j.b 48
861.2.l \(\chi_{861}(419, \cdot)\) 861.2.l.a 216 2
861.2.n \(\chi_{861}(379, \cdot)\) 861.2.n.a 4 4
861.2.n.b 8
861.2.n.c 28
861.2.n.d 36
861.2.n.e 40
861.2.n.f 44
861.2.o \(\chi_{861}(163, \cdot)\) 861.2.o.a 112 2
861.2.r \(\chi_{861}(122, \cdot)\) 861.2.r.a 216 2
861.2.s \(\chi_{861}(206, \cdot)\) 861.2.s.a 106 2
861.2.s.b 106
861.2.v \(\chi_{861}(55, \cdot)\) 861.2.v.a 224 4
861.2.y \(\chi_{861}(260, \cdot)\) 861.2.y.a 336 4
861.2.z \(\chi_{861}(64, \cdot)\) 861.2.z.a 72 4
861.2.z.b 88
861.2.bc \(\chi_{861}(146, \cdot)\) 861.2.bc.a 432 4
861.2.bd \(\chi_{861}(461, \cdot)\) 861.2.bd.a 432 4
861.2.bh \(\chi_{861}(173, \cdot)\) 861.2.bh.a 432 4
861.2.bj \(\chi_{861}(214, \cdot)\) 861.2.bj.a 224 4
861.2.bk \(\chi_{861}(16, \cdot)\) 861.2.bk.a 224 8
861.2.bk.b 224
861.2.bm \(\chi_{861}(20, \cdot)\) 861.2.bm.a 864 8
861.2.bo \(\chi_{861}(43, \cdot)\) 861.2.bo.a 160 8
861.2.bo.b 192
861.2.bp \(\chi_{861}(44, \cdot)\) 861.2.bp.a 864 8
861.2.bs \(\chi_{861}(178, \cdot)\) 861.2.bs.a 448 8
861.2.bv \(\chi_{861}(59, \cdot)\) 861.2.bv.a 864 8
861.2.bw \(\chi_{861}(236, \cdot)\) 861.2.bw.a 864 8
861.2.bz \(\chi_{861}(4, \cdot)\) 861.2.bz.a 448 8
861.2.ca \(\chi_{861}(29, \cdot)\) 861.2.ca.a 1344 16
861.2.cd \(\chi_{861}(13, \cdot)\) 861.2.cd.a 896 16
861.2.ce \(\chi_{861}(46, \cdot)\) 861.2.ce.a 896 16
861.2.cg \(\chi_{861}(5, \cdot)\) 861.2.cg.a 1728 16
861.2.ci \(\chi_{861}(19, \cdot)\) 861.2.ci.a 1792 32
861.2.cl \(\chi_{861}(11, \cdot)\) 861.2.cl.a 3456 32

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(861))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(861)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(123))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(287))\)\(^{\oplus 2}\)