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

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

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 the 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

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