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Properties

Label 936.2
Level 936
Weight 2
Dimension 10447
Nonzero newspaces 45
Newform subspaces 136
Sturm bound 96768
Trace bound 31

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Defining parameters

Level: \( N \) = \( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 45 \)
Newform subspaces: \( 136 \)
Sturm bound: \(96768\)
Trace bound: \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(936))\).

Total New Old
Modular forms 25344 10843 14501
Cusp forms 23041 10447 12594
Eisenstein series 2303 396 1907

Trace form

\( 10447 q - 32 q^{2} - 42 q^{3} - 32 q^{4} - 8 q^{5} - 32 q^{6} - 32 q^{7} - 8 q^{8} - 78 q^{9} + O(q^{10}) \) \( 10447 q - 32 q^{2} - 42 q^{3} - 32 q^{4} - 8 q^{5} - 32 q^{6} - 32 q^{7} - 8 q^{8} - 78 q^{9} - 60 q^{10} - 2 q^{11} - 20 q^{12} + 2 q^{13} - 44 q^{14} - 16 q^{16} - 35 q^{17} - 48 q^{18} - 76 q^{19} - 56 q^{20} + 24 q^{21} - 64 q^{22} - 12 q^{23} - 96 q^{24} - 71 q^{25} - 64 q^{26} - 96 q^{27} - 124 q^{28} - 27 q^{29} - 140 q^{30} - 16 q^{31} - 112 q^{32} - 82 q^{33} - 8 q^{34} - 120 q^{35} - 148 q^{36} - 15 q^{37} - 112 q^{38} - 84 q^{39} - 44 q^{40} - 53 q^{41} - 148 q^{42} - 38 q^{43} - 60 q^{44} - 4 q^{45} - 20 q^{46} - 84 q^{47} - 88 q^{48} + 44 q^{49} + 16 q^{50} - 66 q^{51} + 98 q^{52} + 64 q^{53} - 24 q^{54} - 4 q^{55} + 136 q^{56} - 38 q^{57} + 80 q^{58} - 2 q^{59} + 84 q^{60} + 61 q^{61} + 152 q^{62} - 64 q^{63} + 4 q^{64} + 79 q^{65} + 112 q^{66} + 98 q^{67} + 132 q^{68} + 28 q^{69} + 116 q^{70} + 92 q^{71} + 156 q^{72} - 24 q^{73} + 184 q^{74} - 26 q^{75} + 32 q^{76} + 120 q^{77} + 26 q^{78} + 8 q^{79} + 156 q^{80} - 22 q^{81} - 148 q^{82} + 80 q^{83} + 80 q^{84} + 137 q^{85} + 16 q^{86} + 12 q^{87} - 124 q^{88} + 28 q^{89} - 20 q^{90} + 36 q^{91} - 252 q^{92} + 92 q^{93} - 180 q^{94} + 28 q^{95} - 144 q^{96} - 138 q^{97} - 336 q^{98} - 108 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(936))\)

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
936.2.a \(\chi_{936}(1, \cdot)\) 936.2.a.a 1 1
936.2.a.b 1
936.2.a.c 1
936.2.a.d 1
936.2.a.e 1
936.2.a.f 1
936.2.a.g 1
936.2.a.h 1
936.2.a.i 1
936.2.a.j 2
936.2.a.k 2
936.2.a.l 2
936.2.c \(\chi_{936}(649, \cdot)\) 936.2.c.a 2 1
936.2.c.b 2
936.2.c.c 2
936.2.c.d 4
936.2.c.e 8
936.2.d \(\chi_{936}(287, \cdot)\) None 0 1
936.2.g \(\chi_{936}(469, \cdot)\) 936.2.g.a 2 1
936.2.g.b 4
936.2.g.c 6
936.2.g.d 8
936.2.g.e 16
936.2.g.f 24
936.2.h \(\chi_{936}(467, \cdot)\) 936.2.h.a 56 1
936.2.j \(\chi_{936}(755, \cdot)\) 936.2.j.a 48 1
936.2.m \(\chi_{936}(181, \cdot)\) 936.2.m.a 2 1
936.2.m.b 2
936.2.m.c 2
936.2.m.d 2
936.2.m.e 4
936.2.m.f 8
936.2.m.g 8
936.2.m.h 16
936.2.m.i 24
936.2.n \(\chi_{936}(935, \cdot)\) None 0 1
936.2.q \(\chi_{936}(313, \cdot)\) 936.2.q.a 2 2
936.2.q.b 2
936.2.q.c 2
936.2.q.d 12
936.2.q.e 16
936.2.q.f 16
936.2.q.g 22
936.2.r \(\chi_{936}(601, \cdot)\) 936.2.r.a 2 2
936.2.r.b 2
936.2.r.c 2
936.2.r.d 2
936.2.r.e 36
936.2.r.f 40
936.2.s \(\chi_{936}(529, \cdot)\) 936.2.s.a 2 2
936.2.s.b 2
936.2.s.c 2
936.2.s.d 2
936.2.s.e 36
936.2.s.f 40
936.2.t \(\chi_{936}(217, \cdot)\) 936.2.t.a 2 2
936.2.t.b 2
936.2.t.c 2
936.2.t.d 2
936.2.t.e 4
936.2.t.f 4
936.2.t.g 6
936.2.t.h 6
936.2.t.i 6
936.2.w \(\chi_{936}(307, \cdot)\) 936.2.w.a 2 2
936.2.w.b 2
936.2.w.c 2
936.2.w.d 2
936.2.w.e 4
936.2.w.f 4
936.2.w.g 4
936.2.w.h 20
936.2.w.i 24
936.2.w.j 24
936.2.w.k 48
936.2.x \(\chi_{936}(343, \cdot)\) None 0 2
936.2.ba \(\chi_{936}(161, \cdot)\) 936.2.ba.a 4 2
936.2.ba.b 12
936.2.ba.c 12
936.2.bb \(\chi_{936}(125, \cdot)\) 936.2.bb.a 112 2
936.2.bd \(\chi_{936}(179, \cdot)\) 936.2.bd.a 8 2
936.2.bd.b 8
936.2.bd.c 96
936.2.be \(\chi_{936}(685, \cdot)\) 936.2.be.a 24 2
936.2.be.b 56
936.2.be.c 56
936.2.bh \(\chi_{936}(503, \cdot)\) None 0 2
936.2.bi \(\chi_{936}(361, \cdot)\) 936.2.bi.a 4 2
936.2.bi.b 8
936.2.bi.c 8
936.2.bi.d 16
936.2.bk \(\chi_{936}(277, \cdot)\) 936.2.bk.a 4 2
936.2.bk.b 4
936.2.bk.c 320
936.2.bn \(\chi_{936}(419, \cdot)\) 936.2.bn.a 328 2
936.2.bp \(\chi_{936}(95, \cdot)\) None 0 2
936.2.br \(\chi_{936}(311, \cdot)\) None 0 2
936.2.bv \(\chi_{936}(347, \cdot)\) 936.2.bv.a 328 2
936.2.bx \(\chi_{936}(493, \cdot)\) 936.2.bx.a 328 2
936.2.by \(\chi_{936}(131, \cdot)\) 936.2.by.a 288 2
936.2.ca \(\chi_{936}(205, \cdot)\) 936.2.ca.a 4 2
936.2.ca.b 4
936.2.ca.c 320
936.2.ce \(\chi_{936}(23, \cdot)\) None 0 2
936.2.cg \(\chi_{936}(191, \cdot)\) None 0 2
936.2.ch \(\chi_{936}(49, \cdot)\) 936.2.ch.a 84 2
936.2.cj \(\chi_{936}(133, \cdot)\) 936.2.cj.a 328 2
936.2.cl \(\chi_{936}(155, \cdot)\) 936.2.cl.a 24 2
936.2.cl.b 304
936.2.co \(\chi_{936}(157, \cdot)\) 936.2.co.a 4 2
936.2.co.b 284
936.2.cq \(\chi_{936}(563, \cdot)\) 936.2.cq.a 4 2
936.2.cq.b 324
936.2.cr \(\chi_{936}(121, \cdot)\) 936.2.cr.a 84 2
936.2.ct \(\chi_{936}(599, \cdot)\) None 0 2
936.2.cw \(\chi_{936}(25, \cdot)\) 936.2.cw.a 4 2
936.2.cw.b 80
936.2.cy \(\chi_{936}(263, \cdot)\) None 0 2
936.2.da \(\chi_{936}(491, \cdot)\) 936.2.da.a 4 2
936.2.da.b 324
936.2.db \(\chi_{936}(61, \cdot)\) 936.2.db.a 328 2
936.2.df \(\chi_{936}(647, \cdot)\) None 0 2
936.2.dg \(\chi_{936}(829, \cdot)\) 936.2.dg.a 4 2
936.2.dg.b 4
936.2.dg.c 8
936.2.dg.d 16
936.2.dg.e 48
936.2.dg.f 56
936.2.dj \(\chi_{936}(35, \cdot)\) 936.2.dj.a 112 2
936.2.dk \(\chi_{936}(31, \cdot)\) None 0 4
936.2.dl \(\chi_{936}(187, \cdot)\) 936.2.dl.a 656 4
936.2.dq \(\chi_{936}(197, \cdot)\) 936.2.dq.a 224 4
936.2.dr \(\chi_{936}(89, \cdot)\) 936.2.dr.a 24 4
936.2.dr.b 32
936.2.ds \(\chi_{936}(353, \cdot)\) 936.2.ds.a 168 4
936.2.dt \(\chi_{936}(149, \cdot)\) 936.2.dt.a 656 4
936.2.dy \(\chi_{936}(461, \cdot)\) 936.2.dy.a 656 4
936.2.dz \(\chi_{936}(41, \cdot)\) 936.2.dz.a 168 4
936.2.ec \(\chi_{936}(271, \cdot)\) None 0 4
936.2.ed \(\chi_{936}(19, \cdot)\) 936.2.ed.a 4 4
936.2.ed.b 4
936.2.ed.c 48
936.2.ed.d 48
936.2.ed.e 56
936.2.ed.f 112
936.2.ee \(\chi_{936}(115, \cdot)\) 936.2.ee.a 656 4
936.2.ef \(\chi_{936}(175, \cdot)\) None 0 4
936.2.ek \(\chi_{936}(7, \cdot)\) None 0 4
936.2.el \(\chi_{936}(67, \cdot)\) 936.2.el.a 656 4
936.2.em \(\chi_{936}(5, \cdot)\) 936.2.em.a 656 4
936.2.en \(\chi_{936}(281, \cdot)\) 936.2.en.a 168 4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(936))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(936)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(312))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(468))\)\(^{\oplus 2}\)