Properties

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

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

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

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 available 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

$$S_{2}^{\mathrm{old}}(\Gamma_1(693)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(99))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(231))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(693))$$$$^{\oplus 1}$$