Properties

Label 630.2
Level 630
Weight 2
Dimension 2402
Nonzero newspaces 30
Newforms 118
Sturm bound 41472
Trace bound 15

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Defining parameters

Level: \( N \) = \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Newforms: \( 118 \)
Sturm bound: \(41472\)
Trace bound: \(15\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(630))\).

Total New Old
Modular forms 11136 2402 8734
Cusp forms 9601 2402 7199
Eisenstein series 1535 0 1535

Trace form

\( 2402q - 6q^{2} - 12q^{3} - 10q^{4} - 16q^{5} + 12q^{6} - 28q^{7} + 6q^{8} + 28q^{9} + O(q^{10}) \) \( 2402q - 6q^{2} - 12q^{3} - 10q^{4} - 16q^{5} + 12q^{6} - 28q^{7} + 6q^{8} + 28q^{9} + 16q^{10} + 28q^{11} + 16q^{12} + 24q^{13} + 56q^{14} + 72q^{15} + 6q^{16} + 132q^{17} + 56q^{18} + 84q^{19} + 40q^{20} + 108q^{21} + 92q^{22} + 168q^{23} + 12q^{24} + 58q^{25} + 72q^{26} + 120q^{27} + 24q^{28} + 108q^{29} + 12q^{30} + 72q^{31} - 6q^{32} + 28q^{33} + 16q^{34} + 86q^{35} - 20q^{36} + 140q^{37} - 72q^{38} - 56q^{39} - 8q^{41} - 64q^{42} + 20q^{43} - 64q^{44} - 112q^{45} - 24q^{46} - 24q^{47} - 20q^{48} + 54q^{49} - 154q^{50} - 132q^{51} - 204q^{53} - 204q^{54} + 64q^{55} - 32q^{56} - 244q^{57} - 20q^{58} - 200q^{59} - 56q^{60} + 88q^{61} - 168q^{62} - 296q^{63} + 2q^{64} - 12q^{65} - 96q^{66} + 204q^{67} - 48q^{68} - 88q^{69} + 42q^{70} + 48q^{71} + 12q^{72} + 172q^{73} - 44q^{74} - 96q^{75} + 88q^{76} - 60q^{77} - 40q^{78} + 136q^{79} - 16q^{80} + 20q^{81} + 44q^{82} - 36q^{83} + 12q^{84} + 48q^{85} + 44q^{86} + 40q^{87} - 28q^{88} - 148q^{89} - 32q^{90} - 108q^{91} - 24q^{92} - 184q^{93} - 160q^{94} - 456q^{95} - 8q^{96} - 216q^{97} - 234q^{98} - 104q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(630))\)

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
630.2.a \(\chi_{630}(1, \cdot)\) 630.2.a.a 1 1
630.2.a.b 1
630.2.a.c 1
630.2.a.d 1
630.2.a.e 1
630.2.a.f 1
630.2.a.g 1
630.2.a.h 1
630.2.a.i 1
630.2.a.j 1
630.2.b \(\chi_{630}(251, \cdot)\) 630.2.b.a 8 1
630.2.b.b 8
630.2.d \(\chi_{630}(629, \cdot)\) 630.2.d.a 4 1
630.2.d.b 4
630.2.d.c 4
630.2.d.d 4
630.2.g \(\chi_{630}(379, \cdot)\) 630.2.g.a 2 1
630.2.g.b 2
630.2.g.c 2
630.2.g.d 2
630.2.g.e 2
630.2.g.f 2
630.2.g.g 4
630.2.i \(\chi_{630}(121, \cdot)\) 630.2.i.a 2 2
630.2.i.b 2
630.2.i.c 2
630.2.i.d 2
630.2.i.e 4
630.2.i.f 12
630.2.i.g 12
630.2.i.h 12
630.2.i.i 16
630.2.j \(\chi_{630}(211, \cdot)\) 630.2.j.a 2 2
630.2.j.b 2
630.2.j.c 2
630.2.j.d 2
630.2.j.e 2
630.2.j.f 4
630.2.j.g 4
630.2.j.h 4
630.2.j.i 6
630.2.j.j 6
630.2.j.k 6
630.2.j.l 8
630.2.k \(\chi_{630}(361, \cdot)\) 630.2.k.a 2 2
630.2.k.b 2
630.2.k.c 2
630.2.k.d 2
630.2.k.e 2
630.2.k.f 2
630.2.k.g 2
630.2.k.h 2
630.2.k.i 4
630.2.k.j 4
630.2.l \(\chi_{630}(331, \cdot)\) 630.2.l.a 2 2
630.2.l.b 2
630.2.l.c 2
630.2.l.d 2
630.2.l.e 4
630.2.l.f 12
630.2.l.g 12
630.2.l.h 12
630.2.l.i 16
630.2.m \(\chi_{630}(197, \cdot)\) 630.2.m.a 4 2
630.2.m.b 4
630.2.m.c 8
630.2.m.d 8
630.2.p \(\chi_{630}(307, \cdot)\) 630.2.p.a 8 2
630.2.p.b 8
630.2.p.c 8
630.2.p.d 16
630.2.r \(\chi_{630}(59, \cdot)\) 630.2.r.a 48 2
630.2.r.b 48
630.2.t \(\chi_{630}(311, \cdot)\) 630.2.t.a 4 2
630.2.t.b 28
630.2.t.c 32
630.2.u \(\chi_{630}(109, \cdot)\) 630.2.u.a 4 2
630.2.u.b 4
630.2.u.c 4
630.2.u.d 8
630.2.u.e 8
630.2.u.f 12
630.2.z \(\chi_{630}(169, \cdot)\) 630.2.z.a 4 2
630.2.z.b 24
630.2.z.c 44
630.2.ba \(\chi_{630}(499, \cdot)\) 630.2.ba.a 96 2
630.2.be \(\chi_{630}(341, \cdot)\) 630.2.be.a 8 2
630.2.be.b 8
630.2.bf \(\chi_{630}(209, \cdot)\) 630.2.bf.a 8 2
630.2.bf.b 8
630.2.bf.c 8
630.2.bf.d 8
630.2.bf.e 32
630.2.bf.f 32
630.2.bi \(\chi_{630}(479, \cdot)\) 630.2.bi.a 48 2
630.2.bi.b 48
630.2.bk \(\chi_{630}(101, \cdot)\) 630.2.bk.a 4 2
630.2.bk.b 28
630.2.bk.c 32
630.2.bl \(\chi_{630}(41, \cdot)\) 630.2.bl.a 32 2
630.2.bl.b 32
630.2.bo \(\chi_{630}(89, \cdot)\) 630.2.bo.a 16 2
630.2.bo.b 16
630.2.bq \(\chi_{630}(79, \cdot)\) 630.2.bq.a 96 2
630.2.bt \(\chi_{630}(317, \cdot)\) 630.2.bt.a 192 4
630.2.bv \(\chi_{630}(73, \cdot)\) 630.2.bv.a 16 4
630.2.bv.b 16
630.2.bv.c 16
630.2.bv.d 32
630.2.bw \(\chi_{630}(103, \cdot)\) 630.2.bw.a 192 4
630.2.bz \(\chi_{630}(13, \cdot)\) 630.2.bz.a 192 4
630.2.ca \(\chi_{630}(113, \cdot)\) 630.2.ca.a 72 4
630.2.ca.b 72
630.2.cd \(\chi_{630}(23, \cdot)\) 630.2.cd.a 192 4
630.2.ce \(\chi_{630}(53, \cdot)\) 630.2.ce.a 16 4
630.2.ce.b 16
630.2.ce.c 32
630.2.cg \(\chi_{630}(157, \cdot)\) 630.2.cg.a 192 4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(630))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(630)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 2}\)