Properties

Label 637.2
Level 637
Weight 2
Dimension 15079
Nonzero newspaces 30
Newform subspaces 142
Sturm bound 65856
Trace bound 3

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Defining parameters

Level: \( N \) = \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Newform subspaces: \( 142 \)
Sturm bound: \(65856\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(637))\).

Total New Old
Modular forms 17184 16145 1039
Cusp forms 15745 15079 666
Eisenstein series 1439 1066 373

Trace form

\( 15079q - 150q^{2} - 152q^{3} - 158q^{4} - 156q^{5} - 168q^{6} - 188q^{7} - 291q^{8} - 178q^{9} + O(q^{10}) \) \( 15079q - 150q^{2} - 152q^{3} - 158q^{4} - 156q^{5} - 168q^{6} - 188q^{7} - 291q^{8} - 178q^{9} - 195q^{10} - 174q^{11} - 226q^{12} - 191q^{13} - 432q^{14} - 312q^{15} - 226q^{16} - 189q^{17} - 255q^{18} - 204q^{19} - 261q^{20} - 230q^{21} - 354q^{22} - 204q^{23} - 324q^{24} - 227q^{25} - 237q^{26} - 446q^{27} - 272q^{28} - 339q^{29} - 360q^{30} - 234q^{31} - 336q^{32} - 282q^{33} - 300q^{34} - 258q^{35} - 410q^{36} - 181q^{37} - 222q^{38} - 204q^{39} - 330q^{40} - 189q^{41} - 174q^{42} - 302q^{43} - 138q^{44} - 165q^{45} - 120q^{46} - 198q^{47} - 150q^{48} - 104q^{49} - 573q^{50} - 198q^{51} - 192q^{52} - 402q^{53} - 234q^{54} - 144q^{55} - 132q^{56} - 402q^{57} - 231q^{58} - 222q^{59} - 390q^{60} - 227q^{61} - 336q^{62} - 300q^{63} - 485q^{64} - 330q^{65} - 750q^{66} - 336q^{67} - 519q^{68} - 414q^{69} - 426q^{70} - 456q^{71} - 288q^{72} - 336q^{73} - 351q^{74} - 346q^{75} - 180q^{76} - 234q^{77} - 237q^{78} - 262q^{79} - 9q^{80} - 10q^{81} + 279q^{82} - 6q^{83} + 232q^{84} + 39q^{85} + 48q^{86} + 264q^{87} + 648q^{88} + 36q^{89} + 756q^{90} - 53q^{91} - 192q^{92} + 282q^{93} + 522q^{94} + 132q^{95} + 768q^{96} + 222q^{97} + 264q^{98} - 156q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(637))\)

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
637.2.a \(\chi_{637}(1, \cdot)\) 637.2.a.a 1 1
637.2.a.b 1
637.2.a.c 1
637.2.a.d 1
637.2.a.e 2
637.2.a.f 2
637.2.a.g 2
637.2.a.h 3
637.2.a.i 3
637.2.a.j 3
637.2.a.k 5
637.2.a.l 5
637.2.a.m 6
637.2.a.n 6
637.2.c \(\chi_{637}(246, \cdot)\) 637.2.c.a 2 1
637.2.c.b 2
637.2.c.c 2
637.2.c.d 6
637.2.c.e 8
637.2.c.f 8
637.2.c.g 16
637.2.e \(\chi_{637}(79, \cdot)\) 637.2.e.a 2 2
637.2.e.b 2
637.2.e.c 2
637.2.e.d 2
637.2.e.e 2
637.2.e.f 4
637.2.e.g 4
637.2.e.h 4
637.2.e.i 6
637.2.e.j 6
637.2.e.k 6
637.2.e.l 6
637.2.e.m 10
637.2.e.n 12
637.2.e.o 12
637.2.f \(\chi_{637}(295, \cdot)\) 637.2.f.a 2 2
637.2.f.b 2
637.2.f.c 4
637.2.f.d 4
637.2.f.e 4
637.2.f.f 4
637.2.f.g 8
637.2.f.h 8
637.2.f.i 8
637.2.f.j 12
637.2.f.k 12
637.2.f.l 16
637.2.g \(\chi_{637}(263, \cdot)\) 637.2.g.a 2 2
637.2.g.b 4
637.2.g.c 4
637.2.g.d 4
637.2.g.e 4
637.2.g.f 4
637.2.g.g 4
637.2.g.h 8
637.2.g.i 8
637.2.g.j 8
637.2.g.k 8
637.2.g.l 12
637.2.g.m 16
637.2.h \(\chi_{637}(165, \cdot)\) 637.2.h.a 2 2
637.2.h.b 4
637.2.h.c 4
637.2.h.d 4
637.2.h.e 4
637.2.h.f 4
637.2.h.g 4
637.2.h.h 8
637.2.h.i 8
637.2.h.j 8
637.2.h.k 8
637.2.h.l 12
637.2.h.m 16
637.2.i \(\chi_{637}(489, \cdot)\) 637.2.i.a 32 2
637.2.i.b 56
637.2.k \(\chi_{637}(459, \cdot)\) 637.2.k.a 2 2
637.2.k.b 2
637.2.k.c 2
637.2.k.d 4
637.2.k.e 4
637.2.k.f 4
637.2.k.g 12
637.2.k.h 12
637.2.k.i 12
637.2.k.j 32
637.2.q \(\chi_{637}(491, \cdot)\) 637.2.q.a 2 2
637.2.q.b 2
637.2.q.c 2
637.2.q.d 4
637.2.q.e 4
637.2.q.f 4
637.2.q.g 12
637.2.q.h 12
637.2.q.i 12
637.2.q.j 32
637.2.r \(\chi_{637}(116, \cdot)\) 637.2.r.a 4 2
637.2.r.b 4
637.2.r.c 4
637.2.r.d 12
637.2.r.e 12
637.2.r.f 16
637.2.r.g 32
637.2.u \(\chi_{637}(30, \cdot)\) 637.2.u.a 2 2
637.2.u.b 2
637.2.u.c 2
637.2.u.d 4
637.2.u.e 4
637.2.u.f 4
637.2.u.g 12
637.2.u.h 12
637.2.u.i 12
637.2.u.j 32
637.2.w \(\chi_{637}(92, \cdot)\) 637.2.w.a 162 6
637.2.w.b 174
637.2.x \(\chi_{637}(19, \cdot)\) 637.2.x.a 28 4
637.2.x.b 32
637.2.x.c 112
637.2.bb \(\chi_{637}(227, \cdot)\) 637.2.bb.a 28 4
637.2.bb.b 32
637.2.bb.c 112
637.2.bc \(\chi_{637}(31, \cdot)\) 637.2.bc.a 24 4
637.2.bc.b 32
637.2.bc.c 112
637.2.bd \(\chi_{637}(97, \cdot)\) 637.2.bd.a 28 4
637.2.bd.b 28
637.2.bd.c 112
637.2.bg \(\chi_{637}(64, \cdot)\) 637.2.bg.a 372 6
637.2.bi \(\chi_{637}(16, \cdot)\) 637.2.bi.a 756 12
637.2.bj \(\chi_{637}(9, \cdot)\) 637.2.bj.a 756 12
637.2.bk \(\chi_{637}(22, \cdot)\) 637.2.bk.a 768 12
637.2.bl \(\chi_{637}(53, \cdot)\) 637.2.bl.a 324 12
637.2.bl.b 348
637.2.bn \(\chi_{637}(34, \cdot)\) 637.2.bn.a 744 12
637.2.bp \(\chi_{637}(88, \cdot)\) 637.2.bp.a 756 12
637.2.bs \(\chi_{637}(25, \cdot)\) 637.2.bs.a 768 12
637.2.bt \(\chi_{637}(36, \cdot)\) 637.2.bt.a 768 12
637.2.bz \(\chi_{637}(4, \cdot)\) 637.2.bz.a 756 12
637.2.cb \(\chi_{637}(6, \cdot)\) 637.2.cb.a 1536 24
637.2.cc \(\chi_{637}(5, \cdot)\) 637.2.cc.a 1536 24
637.2.cd \(\chi_{637}(45, \cdot)\) 637.2.cd.a 1512 24
637.2.ch \(\chi_{637}(24, \cdot)\) 637.2.ch.a 1512 24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(637))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(637)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 2}\)