Properties

Label 945.2
Level 945
Weight 2
Dimension 21108
Nonzero newspaces 48
Newforms 144
Sturm bound 124416
Trace bound 11

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Defining parameters

Level: \( N \) = \( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Newforms: \( 144 \)
Sturm bound: \(124416\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(945))\).

Total New Old
Modular forms 32544 22068 10476
Cusp forms 29665 21108 8557
Eisenstein series 2879 960 1919

Trace form

\(21108q \) \(\mathstrut -\mathstrut 40q^{2} \) \(\mathstrut -\mathstrut 48q^{3} \) \(\mathstrut -\mathstrut 60q^{4} \) \(\mathstrut -\mathstrut 46q^{5} \) \(\mathstrut -\mathstrut 120q^{6} \) \(\mathstrut -\mathstrut 70q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut -\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(21108q \) \(\mathstrut -\mathstrut 40q^{2} \) \(\mathstrut -\mathstrut 48q^{3} \) \(\mathstrut -\mathstrut 60q^{4} \) \(\mathstrut -\mathstrut 46q^{5} \) \(\mathstrut -\mathstrut 120q^{6} \) \(\mathstrut -\mathstrut 70q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut -\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 60q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut +\mathstrut 24q^{12} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut +\mathstrut 42q^{14} \) \(\mathstrut -\mathstrut 150q^{15} \) \(\mathstrut -\mathstrut 52q^{16} \) \(\mathstrut +\mathstrut 80q^{17} \) \(\mathstrut +\mathstrut 12q^{18} \) \(\mathstrut -\mathstrut 24q^{19} \) \(\mathstrut +\mathstrut 60q^{20} \) \(\mathstrut -\mathstrut 192q^{21} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 12q^{23} \) \(\mathstrut -\mathstrut 96q^{24} \) \(\mathstrut -\mathstrut 48q^{25} \) \(\mathstrut -\mathstrut 64q^{26} \) \(\mathstrut -\mathstrut 60q^{27} \) \(\mathstrut -\mathstrut 92q^{28} \) \(\mathstrut -\mathstrut 8q^{29} \) \(\mathstrut -\mathstrut 78q^{30} \) \(\mathstrut -\mathstrut 84q^{31} \) \(\mathstrut +\mathstrut 28q^{32} \) \(\mathstrut -\mathstrut 48q^{33} \) \(\mathstrut +\mathstrut 80q^{34} \) \(\mathstrut -\mathstrut 44q^{35} \) \(\mathstrut -\mathstrut 408q^{36} \) \(\mathstrut +\mathstrut 36q^{37} \) \(\mathstrut +\mathstrut 104q^{38} \) \(\mathstrut -\mathstrut 12q^{39} \) \(\mathstrut -\mathstrut 152q^{40} \) \(\mathstrut -\mathstrut 56q^{41} \) \(\mathstrut -\mathstrut 108q^{42} \) \(\mathstrut -\mathstrut 148q^{43} \) \(\mathstrut -\mathstrut 224q^{44} \) \(\mathstrut -\mathstrut 198q^{45} \) \(\mathstrut -\mathstrut 112q^{46} \) \(\mathstrut -\mathstrut 172q^{47} \) \(\mathstrut -\mathstrut 540q^{48} \) \(\mathstrut -\mathstrut 94q^{49} \) \(\mathstrut -\mathstrut 508q^{50} \) \(\mathstrut -\mathstrut 396q^{51} \) \(\mathstrut -\mathstrut 248q^{52} \) \(\mathstrut -\mathstrut 460q^{53} \) \(\mathstrut -\mathstrut 600q^{54} \) \(\mathstrut -\mathstrut 252q^{55} \) \(\mathstrut -\mathstrut 726q^{56} \) \(\mathstrut -\mathstrut 324q^{57} \) \(\mathstrut -\mathstrut 208q^{58} \) \(\mathstrut -\mathstrut 292q^{59} \) \(\mathstrut -\mathstrut 420q^{60} \) \(\mathstrut -\mathstrut 116q^{61} \) \(\mathstrut -\mathstrut 420q^{62} \) \(\mathstrut -\mathstrut 282q^{63} \) \(\mathstrut -\mathstrut 384q^{64} \) \(\mathstrut -\mathstrut 78q^{65} \) \(\mathstrut -\mathstrut 444q^{66} \) \(\mathstrut -\mathstrut 72q^{67} \) \(\mathstrut -\mathstrut 608q^{68} \) \(\mathstrut -\mathstrut 168q^{69} \) \(\mathstrut -\mathstrut 165q^{70} \) \(\mathstrut -\mathstrut 116q^{71} \) \(\mathstrut -\mathstrut 504q^{72} \) \(\mathstrut -\mathstrut 120q^{73} \) \(\mathstrut -\mathstrut 212q^{74} \) \(\mathstrut -\mathstrut 156q^{75} \) \(\mathstrut -\mathstrut 340q^{76} \) \(\mathstrut -\mathstrut 138q^{77} \) \(\mathstrut -\mathstrut 480q^{78} \) \(\mathstrut -\mathstrut 204q^{79} \) \(\mathstrut -\mathstrut 570q^{80} \) \(\mathstrut -\mathstrut 168q^{81} \) \(\mathstrut -\mathstrut 336q^{82} \) \(\mathstrut -\mathstrut 48q^{83} \) \(\mathstrut -\mathstrut 264q^{84} \) \(\mathstrut -\mathstrut 306q^{85} \) \(\mathstrut -\mathstrut 268q^{86} \) \(\mathstrut -\mathstrut 228q^{87} \) \(\mathstrut -\mathstrut 444q^{88} \) \(\mathstrut -\mathstrut 312q^{89} \) \(\mathstrut -\mathstrut 480q^{90} \) \(\mathstrut -\mathstrut 226q^{91} \) \(\mathstrut -\mathstrut 876q^{92} \) \(\mathstrut -\mathstrut 468q^{93} \) \(\mathstrut -\mathstrut 328q^{94} \) \(\mathstrut -\mathstrut 474q^{95} \) \(\mathstrut -\mathstrut 552q^{96} \) \(\mathstrut -\mathstrut 188q^{97} \) \(\mathstrut -\mathstrut 500q^{98} \) \(\mathstrut -\mathstrut 444q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(945))\)

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
945.2.a \(\chi_{945}(1, \cdot)\) 945.2.a.a 2 1
945.2.a.b 2
945.2.a.c 2
945.2.a.d 2
945.2.a.e 2
945.2.a.f 2
945.2.a.g 2
945.2.a.h 2
945.2.a.i 2
945.2.a.j 2
945.2.a.k 2
945.2.a.l 2
945.2.a.m 4
945.2.a.n 4
945.2.b \(\chi_{945}(566, \cdot)\) 945.2.b.a 10 1
945.2.b.b 10
945.2.b.c 12
945.2.b.d 12
945.2.d \(\chi_{945}(379, \cdot)\) 945.2.d.a 2 1
945.2.d.b 2
945.2.d.c 8
945.2.d.d 10
945.2.d.e 10
945.2.d.f 16
945.2.g \(\chi_{945}(944, \cdot)\) 945.2.g.a 32 1
945.2.g.b 32
945.2.i \(\chi_{945}(316, \cdot)\) 945.2.i.a 2 2
945.2.i.b 2
945.2.i.c 8
945.2.i.d 8
945.2.i.e 12
945.2.i.f 16
945.2.j \(\chi_{945}(541, \cdot)\) 945.2.j.a 2 2
945.2.j.b 2
945.2.j.c 6
945.2.j.d 6
945.2.j.e 10
945.2.j.f 10
945.2.j.g 10
945.2.j.h 10
945.2.j.i 14
945.2.j.j 14
945.2.k \(\chi_{945}(361, \cdot)\) 945.2.k.a 4 2
945.2.k.b 24
945.2.k.c 36
945.2.l \(\chi_{945}(46, \cdot)\) 945.2.l.a 4 2
945.2.l.b 24
945.2.l.c 36
945.2.m \(\chi_{945}(323, \cdot)\) 945.2.m.a 48 2
945.2.m.b 48
945.2.p \(\chi_{945}(433, \cdot)\) 945.2.p.a 16 2
945.2.p.b 48
945.2.p.c 64
945.2.r \(\chi_{945}(424, \cdot)\) 945.2.r.a 4 2
945.2.r.b 84
945.2.t \(\chi_{945}(341, \cdot)\) 945.2.t.a 2 2
945.2.t.b 30
945.2.t.c 32
945.2.u \(\chi_{945}(89, \cdot)\) 945.2.u.a 88 2
945.2.z \(\chi_{945}(314, \cdot)\) 945.2.z.a 8 2
945.2.z.b 80
945.2.bb \(\chi_{945}(269, \cdot)\) 945.2.bb.a 32 2
945.2.bb.b 32
945.2.bb.c 64
945.2.be \(\chi_{945}(206, \cdot)\) 945.2.be.a 2 2
945.2.be.b 30
945.2.be.c 32
945.2.bf \(\chi_{945}(109, \cdot)\) 945.2.bf.a 4 2
945.2.bf.b 4
945.2.bf.c 56
945.2.bf.d 64
945.2.bh \(\chi_{945}(64, \cdot)\) 945.2.bh.a 4 2
945.2.bh.b 4
945.2.bh.c 64
945.2.bj \(\chi_{945}(26, \cdot)\) 945.2.bj.a 2 2
945.2.bj.b 2
945.2.bj.c 2
945.2.bj.d 2
945.2.bj.e 4
945.2.bj.f 4
945.2.bj.g 6
945.2.bj.h 6
945.2.bj.i 8
945.2.bj.j 8
945.2.bj.k 20
945.2.bj.l 20
945.2.bl \(\chi_{945}(251, \cdot)\) 945.2.bl.a 2 2
945.2.bl.b 2
945.2.bl.c 2
945.2.bl.d 2
945.2.bl.e 2
945.2.bl.f 2
945.2.bl.g 2
945.2.bl.h 2
945.2.bl.i 24
945.2.bl.j 24
945.2.bo \(\chi_{945}(289, \cdot)\) 945.2.bo.a 4 2
945.2.bo.b 84
945.2.bq \(\chi_{945}(719, \cdot)\) 945.2.bq.a 88 2
945.2.bs \(\chi_{945}(16, \cdot)\) 945.2.bs.a 276 6
945.2.bs.b 300
945.2.bt \(\chi_{945}(106, \cdot)\) 945.2.bt.a 96 6
945.2.bt.b 96
945.2.bt.c 120
945.2.bt.d 120
945.2.bu \(\chi_{945}(121, \cdot)\) 945.2.bu.a 276 6
945.2.bu.b 300
945.2.bv \(\chi_{945}(73, \cdot)\) 945.2.bv.a 4 4
945.2.bv.b 4
945.2.bv.c 4
945.2.bv.d 4
945.2.bv.e 160
945.2.by \(\chi_{945}(233, \cdot)\) 945.2.by.a 176 4
945.2.ca \(\chi_{945}(368, \cdot)\) 945.2.ca.a 176 4
945.2.cc \(\chi_{945}(82, \cdot)\) 945.2.cc.a 128 4
945.2.cc.b 128
945.2.ce \(\chi_{945}(118, \cdot)\) 945.2.ce.a 176 4
945.2.cf \(\chi_{945}(8, \cdot)\) 945.2.cf.a 144 4
945.2.ch \(\chi_{945}(53, \cdot)\) 945.2.ch.a 128 4
945.2.ch.b 128
945.2.cj \(\chi_{945}(208, \cdot)\) 945.2.cj.a 4 4
945.2.cj.b 4
945.2.cj.c 4
945.2.cj.d 4
945.2.cj.e 160
945.2.cl \(\chi_{945}(164, \cdot)\) 945.2.cl.a 840 6
945.2.cq \(\chi_{945}(59, \cdot)\) 945.2.cq.a 840 6
945.2.cs \(\chi_{945}(104, \cdot)\) 945.2.cs.a 24 6
945.2.cs.b 816
945.2.cu \(\chi_{945}(184, \cdot)\) 945.2.cu.a 840 6
945.2.cx \(\chi_{945}(236, \cdot)\) 945.2.cx.a 288 6
945.2.cx.b 288
945.2.cz \(\chi_{945}(41, \cdot)\) 945.2.cz.a 288 6
945.2.cz.b 288
945.2.db \(\chi_{945}(4, \cdot)\) 945.2.db.a 840 6
945.2.dd \(\chi_{945}(169, \cdot)\) 945.2.dd.a 648 6
945.2.de \(\chi_{945}(101, \cdot)\) 945.2.de.a 288 6
945.2.de.b 288
945.2.dh \(\chi_{945}(23, \cdot)\) 945.2.dh.a 1680 12
945.2.di \(\chi_{945}(13, \cdot)\) 945.2.di.a 1680 12
945.2.dk \(\chi_{945}(157, \cdot)\) 945.2.dk.a 1680 12
945.2.dm \(\chi_{945}(92, \cdot)\) 945.2.dm.a 1296 12
945.2.do \(\chi_{945}(2, \cdot)\) 945.2.do.a 1680 12
945.2.dr \(\chi_{945}(52, \cdot)\) 945.2.dr.a 1680 12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(945))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(945)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 2}\)