Properties

Label 693.2
Level 693
Weight 2
Dimension 12486
Nonzero newspaces 40
Newform subspaces 104
Sturm bound 69120
Trace bound 9

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Defining parameters

Level: \( N \) = \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Newform subspaces: \( 104 \)
Sturm bound: \(69120\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(693))\).

Total New Old
Modular forms 18240 13298 4942
Cusp forms 16321 12486 3835
Eisenstein series 1919 812 1107

Trace form

\( 12486q - 42q^{2} - 56q^{3} - 34q^{4} - 36q^{5} - 56q^{6} - 44q^{7} - 76q^{8} - 56q^{9} + O(q^{10}) \) \( 12486q - 42q^{2} - 56q^{3} - 34q^{4} - 36q^{5} - 56q^{6} - 44q^{7} - 76q^{8} - 56q^{9} - 66q^{10} - 32q^{11} - 160q^{12} - 18q^{13} - 54q^{14} - 176q^{15} - 6q^{16} - 54q^{17} - 104q^{18} - 118q^{19} - 142q^{20} - 112q^{21} - 90q^{22} - 142q^{23} - 188q^{24} - 62q^{25} - 178q^{26} - 152q^{27} - 224q^{28} - 184q^{29} - 260q^{30} - 80q^{31} - 358q^{32} - 192q^{33} - 224q^{34} - 178q^{35} - 412q^{36} - 172q^{37} - 298q^{38} - 188q^{39} - 226q^{40} - 210q^{41} - 268q^{42} - 124q^{43} - 106q^{44} - 252q^{45} - 98q^{46} - 26q^{47} - 112q^{48} - 26q^{49} - 172q^{50} - 76q^{51} - 66q^{52} - 26q^{53} - 156q^{54} - 172q^{55} - 66q^{56} - 216q^{57} - 138q^{58} - 48q^{59} - 132q^{60} - 116q^{61} - 198q^{62} + 12q^{63} - 616q^{64} - 216q^{65} - 286q^{66} - 346q^{67} - 350q^{68} - 168q^{69} - 408q^{70} - 426q^{71} - 248q^{72} - 328q^{73} - 534q^{74} - 220q^{75} - 516q^{76} - 276q^{77} - 624q^{78} - 212q^{79} - 222q^{80} - 224q^{81} - 406q^{82} - 92q^{83} - 274q^{84} - 188q^{85} - 202q^{86} - 36q^{87} - 158q^{88} - 214q^{89} + 20q^{90} - 396q^{91} - 124q^{92} - 84q^{93} - 150q^{94} + 72q^{95} + 164q^{96} - 52q^{97} - 166q^{98} + 48q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(693))\)

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
693.2.a \(\chi_{693}(1, \cdot)\) 693.2.a.a 1 1
693.2.a.b 1
693.2.a.c 1
693.2.a.d 1
693.2.a.e 2
693.2.a.f 2
693.2.a.g 2
693.2.a.h 2
693.2.a.i 2
693.2.a.j 2
693.2.a.k 2
693.2.a.l 3
693.2.a.m 3
693.2.c \(\chi_{693}(307, \cdot)\) 693.2.c.a 2 1
693.2.c.b 4
693.2.c.c 4
693.2.c.d 12
693.2.c.e 16
693.2.e \(\chi_{693}(188, \cdot)\) 693.2.e.a 24 1
693.2.g \(\chi_{693}(197, \cdot)\) 693.2.g.a 24 1
693.2.i \(\chi_{693}(100, \cdot)\) 693.2.i.a 2 2
693.2.i.b 2
693.2.i.c 2
693.2.i.d 2
693.2.i.e 2
693.2.i.f 4
693.2.i.g 6
693.2.i.h 6
693.2.i.i 8
693.2.i.j 10
693.2.i.k 12
693.2.i.l 12
693.2.j \(\chi_{693}(232, \cdot)\) 693.2.j.a 2 2
693.2.j.b 2
693.2.j.c 2
693.2.j.d 6
693.2.j.e 12
693.2.j.f 18
693.2.j.g 20
693.2.j.h 28
693.2.j.i 30
693.2.k \(\chi_{693}(67, \cdot)\) 693.2.k.a 6 2
693.2.k.b 74
693.2.k.c 80
693.2.l \(\chi_{693}(529, \cdot)\) 693.2.l.a 6 2
693.2.l.b 74
693.2.l.c 80
693.2.m \(\chi_{693}(64, \cdot)\) 693.2.m.a 4 4
693.2.m.b 4
693.2.m.c 4
693.2.m.d 4
693.2.m.e 4
693.2.m.f 8
693.2.m.g 8
693.2.m.h 16
693.2.m.i 16
693.2.m.j 20
693.2.m.k 32
693.2.n \(\chi_{693}(320, \cdot)\) 693.2.n.a 160 2
693.2.p \(\chi_{693}(241, \cdot)\) 693.2.p.a 184 2
693.2.r \(\chi_{693}(32, \cdot)\) 693.2.r.a 184 2
693.2.w \(\chi_{693}(428, \cdot)\) 693.2.w.a 144 2
693.2.x \(\chi_{693}(296, \cdot)\) 693.2.x.a 64 2
693.2.ba \(\chi_{693}(439, \cdot)\) 693.2.ba.a 184 2
693.2.bd \(\chi_{693}(419, \cdot)\) 693.2.bd.a 160 2
693.2.be \(\chi_{693}(89, \cdot)\) 693.2.be.a 56 2
693.2.bg \(\chi_{693}(10, \cdot)\) 693.2.bg.a 12 2
693.2.bg.b 32
693.2.bg.c 32
693.2.bj \(\chi_{693}(76, \cdot)\) 693.2.bj.a 184 2
693.2.bk \(\chi_{693}(122, \cdot)\) 693.2.bk.a 160 2
693.2.bn \(\chi_{693}(263, \cdot)\) 693.2.bn.a 184 2
693.2.bq \(\chi_{693}(8, \cdot)\) 693.2.bq.a 96 4
693.2.bs \(\chi_{693}(125, \cdot)\) 693.2.bs.a 32 4
693.2.bs.b 96
693.2.bu \(\chi_{693}(118, \cdot)\) 693.2.bu.a 8 4
693.2.bu.b 16
693.2.bu.c 16
693.2.bu.d 16
693.2.bu.e 32
693.2.bu.f 64
693.2.bw \(\chi_{693}(25, \cdot)\) 693.2.bw.a 736 8
693.2.bx \(\chi_{693}(4, \cdot)\) 693.2.bx.a 736 8
693.2.by \(\chi_{693}(37, \cdot)\) 693.2.by.a 8 8
693.2.by.b 40
693.2.by.c 64
693.2.by.d 64
693.2.by.e 128
693.2.bz \(\chi_{693}(148, \cdot)\) 693.2.bz.a 288 8
693.2.bz.b 288
693.2.cb \(\chi_{693}(74, \cdot)\) 693.2.cb.a 736 8
693.2.ce \(\chi_{693}(47, \cdot)\) 693.2.ce.a 736 8
693.2.cg \(\chi_{693}(19, \cdot)\) 693.2.cg.a 48 8
693.2.cg.b 128
693.2.cg.c 128
693.2.ch \(\chi_{693}(13, \cdot)\) 693.2.ch.a 736 8
693.2.cj \(\chi_{693}(20, \cdot)\) 693.2.cj.a 736 8
693.2.cm \(\chi_{693}(26, \cdot)\) 693.2.cm.a 256 8
693.2.co \(\chi_{693}(61, \cdot)\) 693.2.co.a 736 8
693.2.cq \(\chi_{693}(29, \cdot)\) 693.2.cq.a 576 8
693.2.ct \(\chi_{693}(107, \cdot)\) 693.2.ct.a 256 8
693.2.cx \(\chi_{693}(2, \cdot)\) 693.2.cx.a 736 8
693.2.cz \(\chi_{693}(40, \cdot)\) 693.2.cz.a 736 8
693.2.db \(\chi_{693}(5, \cdot)\) 693.2.db.a 736 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(693))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(693)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 2}\)