Properties

Label 945.2
Level 945
Weight 2
Dimension 21108
Nonzero newspaces 48
Newform subspaces 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: \( 48 \)
Newform subspaces: \( 144 \)
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

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

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

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