Properties

Label 1260.2
Level 1260
Weight 2
Dimension 16558
Nonzero newspaces 60
Sturm bound 165888
Trace bound 25

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Defining parameters

Level: \( N \) = \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(165888\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1260))\).

Total New Old
Modular forms 43392 17094 26298
Cusp forms 39553 16558 22995
Eisenstein series 3839 536 3303

Trace form

\( 16558q - 18q^{2} - 30q^{4} - 43q^{5} - 52q^{6} - 42q^{8} - 72q^{9} + O(q^{10}) \) \( 16558q - 18q^{2} - 30q^{4} - 43q^{5} - 52q^{6} - 42q^{8} - 72q^{9} - 78q^{10} - 50q^{11} + 16q^{12} - 108q^{13} - 6q^{14} - 18q^{15} - 18q^{16} - 86q^{17} + 80q^{18} - 82q^{19} + 98q^{20} - 154q^{21} + 72q^{22} - 18q^{23} + 60q^{24} - 59q^{25} + 148q^{26} + 12q^{27} + 50q^{28} - 24q^{29} + 54q^{30} + 38q^{31} + 122q^{32} + 156q^{33} + 216q^{34} + 77q^{35} - 60q^{36} - 10q^{37} + 160q^{38} + 172q^{39} + 162q^{40} + 272q^{41} + 92q^{42} + 112q^{43} + 204q^{44} + 198q^{45} + 128q^{46} + 234q^{47} + 164q^{48} + 120q^{49} - 10q^{50} + 240q^{51} + 152q^{52} + 358q^{53} + 80q^{54} + 94q^{55} + 70q^{56} + 200q^{57} + 44q^{58} + 202q^{59} - 122q^{60} + 86q^{61} - 128q^{62} + 166q^{63} - 114q^{64} + 242q^{65} - 284q^{66} - 34q^{67} - 280q^{68} + 76q^{69} + 6q^{70} + 24q^{71} - 432q^{72} + 90q^{73} - 468q^{74} - 42q^{75} - 152q^{76} + 276q^{77} - 520q^{78} + 102q^{79} - 350q^{80} - 72q^{81} - 52q^{82} - 24q^{83} - 340q^{84} + 150q^{85} - 404q^{86} - 152q^{87} - 168q^{88} + 266q^{89} - 426q^{90} + 128q^{91} - 484q^{92} + 184q^{93} - 156q^{94} + 69q^{95} - 448q^{96} + 436q^{97} - 342q^{98} - 44q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1260))\)

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
1260.2.a \(\chi_{1260}(1, \cdot)\) 1260.2.a.a 1 1
1260.2.a.b 1
1260.2.a.c 1
1260.2.a.d 1
1260.2.a.e 1
1260.2.a.f 1
1260.2.a.g 1
1260.2.a.h 1
1260.2.a.i 1
1260.2.a.j 1
1260.2.c \(\chi_{1260}(811, \cdot)\) 1260.2.c.a 4 1
1260.2.c.b 4
1260.2.c.c 8
1260.2.c.d 16
1260.2.c.e 16
1260.2.c.f 32
1260.2.d \(\chi_{1260}(881, \cdot)\) 1260.2.d.a 4 1
1260.2.d.b 4
1260.2.f \(\chi_{1260}(629, \cdot)\) 1260.2.f.a 8 1
1260.2.f.b 8
1260.2.i \(\chi_{1260}(559, \cdot)\) n/a 116 1
1260.2.k \(\chi_{1260}(1009, \cdot)\) 1260.2.k.a 2 1
1260.2.k.b 2
1260.2.k.c 2
1260.2.k.d 2
1260.2.k.e 8
1260.2.l \(\chi_{1260}(1079, \cdot)\) 1260.2.l.a 4 1
1260.2.l.b 4
1260.2.l.c 32
1260.2.l.d 32
1260.2.n \(\chi_{1260}(71, \cdot)\) 1260.2.n.a 24 1
1260.2.n.b 24
1260.2.q \(\chi_{1260}(121, \cdot)\) 1260.2.q.a 2 2
1260.2.q.b 2
1260.2.q.c 2
1260.2.q.d 26
1260.2.q.e 32
1260.2.r \(\chi_{1260}(421, \cdot)\) 1260.2.r.a 2 2
1260.2.r.b 2
1260.2.r.c 2
1260.2.r.d 2
1260.2.r.e 2
1260.2.r.f 8
1260.2.r.g 8
1260.2.r.h 8
1260.2.r.i 14
1260.2.s \(\chi_{1260}(361, \cdot)\) 1260.2.s.a 2 2
1260.2.s.b 2
1260.2.s.c 2
1260.2.s.d 2
1260.2.s.e 4
1260.2.s.f 4
1260.2.s.g 6
1260.2.s.h 6
1260.2.t \(\chi_{1260}(961, \cdot)\) 1260.2.t.a 2 2
1260.2.t.b 2
1260.2.t.c 2
1260.2.t.d 26
1260.2.t.e 32
1260.2.v \(\chi_{1260}(197, \cdot)\) 1260.2.v.a 12 2
1260.2.v.b 12
1260.2.w \(\chi_{1260}(127, \cdot)\) n/a 180 2
1260.2.z \(\chi_{1260}(503, \cdot)\) n/a 192 2
1260.2.ba \(\chi_{1260}(433, \cdot)\) 1260.2.ba.a 8 2
1260.2.ba.b 16
1260.2.ba.c 16
1260.2.bc \(\chi_{1260}(439, \cdot)\) n/a 560 2
1260.2.bf \(\chi_{1260}(689, \cdot)\) 1260.2.bf.a 96 2
1260.2.bh \(\chi_{1260}(941, \cdot)\) 1260.2.bh.a 2 2
1260.2.bh.b 2
1260.2.bh.c 2
1260.2.bh.d 28
1260.2.bh.e 30
1260.2.bi \(\chi_{1260}(31, \cdot)\) n/a 384 2
1260.2.bl \(\chi_{1260}(179, \cdot)\) n/a 192 2
1260.2.bm \(\chi_{1260}(109, \cdot)\) 1260.2.bm.a 4 2
1260.2.bm.b 4
1260.2.bm.c 16
1260.2.bm.d 16
1260.2.bo \(\chi_{1260}(491, \cdot)\) n/a 288 2
1260.2.bs \(\chi_{1260}(11, \cdot)\) n/a 384 2
1260.2.bv \(\chi_{1260}(169, \cdot)\) 1260.2.bv.a 4 2
1260.2.bv.b 68
1260.2.bx \(\chi_{1260}(779, \cdot)\) n/a 560 2
1260.2.by \(\chi_{1260}(529, \cdot)\) 1260.2.by.a 4 2
1260.2.by.b 92
1260.2.ca \(\chi_{1260}(239, \cdot)\) n/a 432 2
1260.2.ce \(\chi_{1260}(431, \cdot)\) n/a 128 2
1260.2.cg \(\chi_{1260}(341, \cdot)\) 1260.2.cg.a 12 2
1260.2.cg.b 12
1260.2.ch \(\chi_{1260}(271, \cdot)\) n/a 160 2
1260.2.cj \(\chi_{1260}(209, \cdot)\) 1260.2.cj.a 8 2
1260.2.cj.b 8
1260.2.cj.c 80
1260.2.cl \(\chi_{1260}(619, \cdot)\) n/a 560 2
1260.2.co \(\chi_{1260}(509, \cdot)\) 1260.2.co.a 96 2
1260.2.cq \(\chi_{1260}(139, \cdot)\) n/a 560 2
1260.2.cs \(\chi_{1260}(391, \cdot)\) n/a 384 2
1260.2.cu \(\chi_{1260}(101, \cdot)\) 1260.2.cu.a 2 2
1260.2.cu.b 2
1260.2.cu.c 2
1260.2.cu.d 28
1260.2.cu.e 30
1260.2.cv \(\chi_{1260}(871, \cdot)\) n/a 384 2
1260.2.cx \(\chi_{1260}(41, \cdot)\) 1260.2.cx.a 2 2
1260.2.cx.b 2
1260.2.cx.c 30
1260.2.cx.d 30
1260.2.cz \(\chi_{1260}(19, \cdot)\) n/a 232 2
1260.2.dc \(\chi_{1260}(89, \cdot)\) 1260.2.dc.a 32 2
1260.2.df \(\chi_{1260}(191, \cdot)\) n/a 384 2
1260.2.dh \(\chi_{1260}(599, \cdot)\) n/a 560 2
1260.2.di \(\chi_{1260}(709, \cdot)\) 1260.2.di.a 4 2
1260.2.di.b 92
1260.2.dl \(\chi_{1260}(67, \cdot)\) n/a 1120 4
1260.2.dm \(\chi_{1260}(317, \cdot)\) n/a 192 4
1260.2.do \(\chi_{1260}(83, \cdot)\) n/a 1120 4
1260.2.dq \(\chi_{1260}(73, \cdot)\) 1260.2.dq.a 16 4
1260.2.dq.b 32
1260.2.dq.c 32
1260.2.ds \(\chi_{1260}(493, \cdot)\) n/a 192 4
1260.2.dv \(\chi_{1260}(227, \cdot)\) n/a 1120 4
1260.2.dx \(\chi_{1260}(143, \cdot)\) n/a 384 4
1260.2.dz \(\chi_{1260}(13, \cdot)\) n/a 192 4
1260.2.ea \(\chi_{1260}(113, \cdot)\) n/a 144 4
1260.2.ec \(\chi_{1260}(163, \cdot)\) n/a 464 4
1260.2.ee \(\chi_{1260}(247, \cdot)\) n/a 1120 4
1260.2.eh \(\chi_{1260}(137, \cdot)\) n/a 192 4
1260.2.ej \(\chi_{1260}(53, \cdot)\) 1260.2.ej.a 64 4
1260.2.el \(\chi_{1260}(43, \cdot)\) n/a 864 4
1260.2.en \(\chi_{1260}(157, \cdot)\) n/a 192 4
1260.2.eo \(\chi_{1260}(47, \cdot)\) n/a 1120 4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1260))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1260)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(420))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(630))\)\(^{\oplus 2}\)