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Properties

Label 671.2
Level 671
Weight 2
Dimension 17747
Nonzero newspaces 42
Newform subspaces 54
Sturm bound 74400
Trace bound 6

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Defining parameters

Level: \( N \) = \( 671 = 11 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 42 \)
Newform subspaces: \( 54 \)
Sturm bound: \(74400\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(671))\).

Total New Old
Modular forms 19200 18811 389
Cusp forms 18001 17747 254
Eisenstein series 1199 1064 135

Trace form

\( 17747 q - 239 q^{2} - 242 q^{3} - 251 q^{4} - 248 q^{5} - 256 q^{6} - 244 q^{7} - 255 q^{8} - 249 q^{9} + O(q^{10}) \) \( 17747 q - 239 q^{2} - 242 q^{3} - 251 q^{4} - 248 q^{5} - 256 q^{6} - 244 q^{7} - 255 q^{8} - 249 q^{9} - 254 q^{10} - 273 q^{11} - 564 q^{12} - 262 q^{13} - 272 q^{14} - 262 q^{15} - 263 q^{16} - 254 q^{17} - 287 q^{18} - 260 q^{19} - 286 q^{20} - 276 q^{21} - 269 q^{22} - 562 q^{23} - 300 q^{24} - 263 q^{25} - 266 q^{26} - 290 q^{27} - 288 q^{28} - 270 q^{29} - 316 q^{30} - 286 q^{31} - 319 q^{32} - 272 q^{33} - 602 q^{34} - 284 q^{35} - 323 q^{36} - 284 q^{37} - 300 q^{38} - 288 q^{39} - 330 q^{40} - 266 q^{41} - 328 q^{42} - 272 q^{43} - 281 q^{44} - 614 q^{45} - 316 q^{46} - 244 q^{47} - 172 q^{48} - 151 q^{49} - 199 q^{50} - 196 q^{51} + 96 q^{52} - 222 q^{53} + 20 q^{54} - 158 q^{55} - 300 q^{56} - 80 q^{57} - 90 q^{58} - 190 q^{59} + 136 q^{60} - 53 q^{61} - 188 q^{62} - 92 q^{63} + 129 q^{64} - 212 q^{65} - 166 q^{66} - 354 q^{67} + 2 q^{68} - 98 q^{69} - 32 q^{70} - 246 q^{71} + 15 q^{72} - 202 q^{73} - 192 q^{74} - 232 q^{75} - 180 q^{76} - 244 q^{77} - 724 q^{78} - 300 q^{79} - 418 q^{80} - 363 q^{81} - 398 q^{82} - 312 q^{83} - 472 q^{84} - 344 q^{85} - 396 q^{86} - 360 q^{87} - 285 q^{88} - 660 q^{89} - 482 q^{90} - 336 q^{91} - 404 q^{92} - 354 q^{93} - 352 q^{94} - 360 q^{95} - 476 q^{96} - 324 q^{97} - 423 q^{98} - 279 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(671))\)

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
671.2.a \(\chi_{671}(1, \cdot)\) 671.2.a.a 5 1
671.2.a.b 6
671.2.a.c 19
671.2.a.d 21
671.2.c \(\chi_{671}(243, \cdot)\) 671.2.c.a 52 1
671.2.e \(\chi_{671}(474, \cdot)\) 671.2.e.a 52 2
671.2.e.b 52
671.2.f \(\chi_{671}(538, \cdot)\) 671.2.f.a 120 2
671.2.h \(\chi_{671}(70, \cdot)\) 671.2.h.a 4 4
671.2.h.b 236
671.2.i \(\chi_{671}(34, \cdot)\) 671.2.i.a 108 4
671.2.i.b 108
671.2.j \(\chi_{671}(245, \cdot)\) 671.2.j.a 4 4
671.2.j.b 108
671.2.j.c 128
671.2.k \(\chi_{671}(180, \cdot)\) 671.2.k.a 4 4
671.2.k.b 236
671.2.l \(\chi_{671}(9, \cdot)\) 671.2.l.a 4 4
671.2.l.b 236
671.2.m \(\chi_{671}(20, \cdot)\) 671.2.m.a 4 4
671.2.m.b 236
671.2.o \(\chi_{671}(353, \cdot)\) 671.2.o.a 100 2
671.2.q \(\chi_{671}(113, \cdot)\) 671.2.q.a 240 4
671.2.x \(\chi_{671}(60, \cdot)\) 671.2.x.a 240 4
671.2.ba \(\chi_{671}(64, \cdot)\) 671.2.ba.a 240 4
671.2.bc \(\chi_{671}(210, \cdot)\) 671.2.bc.a 208 4
671.2.bd \(\chi_{671}(102, \cdot)\) 671.2.bd.a 240 4
671.2.bf \(\chi_{671}(3, \cdot)\) 671.2.bf.a 240 4
671.2.bj \(\chi_{671}(21, \cdot)\) 671.2.bj.a 240 4
671.2.bk \(\chi_{671}(15, \cdot)\) 671.2.bk.a 480 8
671.2.bl \(\chi_{671}(25, \cdot)\) 671.2.bl.a 480 8
671.2.bm \(\chi_{671}(47, \cdot)\) 671.2.bm.a 480 8
671.2.bn \(\chi_{671}(12, \cdot)\) 671.2.bn.a 208 8
671.2.bn.b 208
671.2.bo \(\chi_{671}(16, \cdot)\) 671.2.bo.a 480 8
671.2.bp \(\chi_{671}(137, \cdot)\) 671.2.bp.a 480 8
671.2.br \(\chi_{671}(145, \cdot)\) 671.2.br.a 480 8
671.2.bt \(\chi_{671}(24, \cdot)\) 671.2.bt.a 480 8
671.2.bv \(\chi_{671}(85, \cdot)\) 671.2.bv.a 480 8
671.2.bw \(\chi_{671}(98, \cdot)\) 671.2.bw.a 480 8
671.2.by \(\chi_{671}(8, \cdot)\) 671.2.by.a 480 8
671.2.cb \(\chi_{671}(50, \cdot)\) 671.2.cb.a 480 8
671.2.ce \(\chi_{671}(5, \cdot)\) 671.2.ce.a 480 8
671.2.cf \(\chi_{671}(45, \cdot)\) 671.2.cf.a 400 8
671.2.ch \(\chi_{671}(4, \cdot)\) 671.2.ch.a 480 8
671.2.ck \(\chi_{671}(14, \cdot)\) 671.2.ck.a 480 8
671.2.cm \(\chi_{671}(49, \cdot)\) 671.2.cm.a 480 8
671.2.ct \(\chi_{671}(97, \cdot)\) 671.2.ct.a 480 8
671.2.cu \(\chi_{671}(7, \cdot)\) 671.2.cu.a 960 16
671.2.cw \(\chi_{671}(29, \cdot)\) 671.2.cw.a 960 16
671.2.cz \(\chi_{671}(2, \cdot)\) 671.2.cz.a 960 16
671.2.db \(\chi_{671}(10, \cdot)\) 671.2.db.a 960 16
671.2.dc \(\chi_{671}(6, \cdot)\) 671.2.dc.a 960 16
671.2.de \(\chi_{671}(18, \cdot)\) 671.2.de.a 960 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(671))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(671)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(61))\)\(^{\oplus 2}\)