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Properties

Label 663.2
Level 663
Weight 2
Dimension 11543
Nonzero newspaces 36
Newform subspaces 78
Sturm bound 64512
Trace bound 17

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Defining parameters

Level: \( N \) = \( 663 = 3 \cdot 13 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Newform subspaces: \( 78 \)
Sturm bound: \(64512\)
Trace bound: \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(663))\).

Total New Old
Modular forms 16896 12199 4697
Cusp forms 15361 11543 3818
Eisenstein series 1535 656 879

Trace form

\( 11543 q + 9 q^{2} - 65 q^{3} - 115 q^{4} + 18 q^{5} - 59 q^{6} - 120 q^{7} + 9 q^{8} - 69 q^{9} + O(q^{10}) \) \( 11543 q + 9 q^{2} - 65 q^{3} - 115 q^{4} + 18 q^{5} - 59 q^{6} - 120 q^{7} + 9 q^{8} - 69 q^{9} - 158 q^{10} - 20 q^{11} - 147 q^{12} - 189 q^{13} - 40 q^{14} - 122 q^{15} - 267 q^{16} - 15 q^{17} - 251 q^{18} - 188 q^{19} - 118 q^{20} - 144 q^{21} - 212 q^{22} - 8 q^{23} - 175 q^{24} - 239 q^{25} - 111 q^{26} - 221 q^{27} - 328 q^{28} - 50 q^{29} - 190 q^{30} - 216 q^{31} - 91 q^{32} - 124 q^{33} - 347 q^{34} - 32 q^{35} - 51 q^{36} - 162 q^{37} + 20 q^{38} - 33 q^{39} - 386 q^{40} - 38 q^{41} - 32 q^{42} - 228 q^{43} + 4 q^{44} + 22 q^{45} - 224 q^{46} + 48 q^{47} + 65 q^{48} - 141 q^{49} + 51 q^{50} - 29 q^{51} - 439 q^{52} - 78 q^{53} - 123 q^{54} - 312 q^{55} - 160 q^{56} - 188 q^{57} - 390 q^{58} - 116 q^{59} - 226 q^{60} - 370 q^{61} - 200 q^{62} - 240 q^{63} - 423 q^{64} - 138 q^{65} - 228 q^{66} - 220 q^{67} - 245 q^{68} - 312 q^{69} - 512 q^{70} - 24 q^{71} - 203 q^{72} - 394 q^{73} - 150 q^{74} - 235 q^{75} - 420 q^{76} - 176 q^{77} - 55 q^{78} - 464 q^{79} - 262 q^{80} - 109 q^{81} - 394 q^{82} - 44 q^{83} - 208 q^{84} - 268 q^{85} + 76 q^{86} - 26 q^{87} - 388 q^{88} - 66 q^{89} + 70 q^{90} - 328 q^{91} - 152 q^{92} - 32 q^{93} - 392 q^{94} - 104 q^{95} - 27 q^{96} - 234 q^{97} + 57 q^{98} - 108 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(663))\)

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
663.2.a \(\chi_{663}(1, \cdot)\) 663.2.a.a 1 1
663.2.a.b 1
663.2.a.c 1
663.2.a.d 3
663.2.a.e 3
663.2.a.f 5
663.2.a.g 5
663.2.a.h 6
663.2.a.i 6
663.2.b \(\chi_{663}(103, \cdot)\) 663.2.b.a 2 1
663.2.b.b 2
663.2.b.c 6
663.2.b.d 8
663.2.b.e 8
663.2.b.f 10
663.2.e \(\chi_{663}(220, \cdot)\) 663.2.e.a 40 1
663.2.f \(\chi_{663}(118, \cdot)\) 663.2.f.a 2 1
663.2.f.b 16
663.2.f.c 18
663.2.i \(\chi_{663}(256, \cdot)\) 663.2.i.a 2 2
663.2.i.b 2
663.2.i.c 2
663.2.i.d 2
663.2.i.e 12
663.2.i.f 16
663.2.i.g 18
663.2.i.h 22
663.2.j \(\chi_{663}(157, \cdot)\) 663.2.j.a 32 2
663.2.j.b 40
663.2.m \(\chi_{663}(200, \cdot)\) 663.2.m.a 160 2
663.2.n \(\chi_{663}(86, \cdot)\) 663.2.n.a 76 2
663.2.n.b 76
663.2.q \(\chi_{663}(203, \cdot)\) 663.2.q.a 8 2
663.2.q.b 8
663.2.q.c 144
663.2.r \(\chi_{663}(47, \cdot)\) 663.2.r.a 160 2
663.2.u \(\chi_{663}(64, \cdot)\) 663.2.u.a 80 2
663.2.w \(\chi_{663}(16, \cdot)\) 663.2.w.a 4 2
663.2.w.b 8
663.2.w.c 76
663.2.z \(\chi_{663}(205, \cdot)\) 663.2.z.a 2 2
663.2.z.b 4
663.2.z.c 12
663.2.z.d 16
663.2.z.e 20
663.2.z.f 22
663.2.ba \(\chi_{663}(322, \cdot)\) 663.2.ba.a 80 2
663.2.bd \(\chi_{663}(8, \cdot)\) 663.2.bd.a 4 4
663.2.bd.b 4
663.2.bd.c 312
663.2.bg \(\chi_{663}(196, \cdot)\) 663.2.bg.a 64 4
663.2.bg.b 80
663.2.bh \(\chi_{663}(25, \cdot)\) 663.2.bh.a 176 4
663.2.bi \(\chi_{663}(161, \cdot)\) 663.2.bi.a 4 4
663.2.bi.b 4
663.2.bi.c 312
663.2.bk \(\chi_{663}(4, \cdot)\) 663.2.bk.a 160 4
663.2.bm \(\chi_{663}(89, \cdot)\) 663.2.bm.a 320 4
663.2.bp \(\chi_{663}(50, \cdot)\) 663.2.bp.a 8 4
663.2.bp.b 8
663.2.bp.c 304
663.2.bq \(\chi_{663}(137, \cdot)\) 663.2.bq.a 148 4
663.2.bq.b 148
663.2.bt \(\chi_{663}(98, \cdot)\) 663.2.bt.a 320 4
663.2.bv \(\chi_{663}(55, \cdot)\) 663.2.bv.a 176 4
663.2.bx \(\chi_{663}(116, \cdot)\) 663.2.bx.a 640 8
663.2.by \(\chi_{663}(14, \cdot)\) 663.2.by.a 288 8
663.2.by.b 288
663.2.ca \(\chi_{663}(31, \cdot)\) 663.2.ca.a 336 8
663.2.cd \(\chi_{663}(73, \cdot)\) 663.2.cd.a 336 8
663.2.cf \(\chi_{663}(110, \cdot)\) 663.2.cf.a 640 8
663.2.cg \(\chi_{663}(94, \cdot)\) 663.2.cg.a 320 8
663.2.ch \(\chi_{663}(43, \cdot)\) 663.2.ch.a 352 8
663.2.ck \(\chi_{663}(2, \cdot)\) 663.2.ck.a 640 8
663.2.cm \(\chi_{663}(7, \cdot)\) 663.2.cm.a 672 16
663.2.cp \(\chi_{663}(28, \cdot)\) 663.2.cp.a 672 16
663.2.cr \(\chi_{663}(29, \cdot)\) 663.2.cr.a 1280 16
663.2.cs \(\chi_{663}(23, \cdot)\) 663.2.cs.a 1280 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(663))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(663)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(221))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(663))\)\(^{\oplus 1}\)