Properties

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

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 861 = 3 \cdot 7 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Newforms: \( 65 \)
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

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

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 the 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

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