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Properties

Label 1560.2
Level 1560
Weight 2
Dimension 24388
Nonzero newspaces 60
Sturm bound 258048
Trace bound 31

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Defining parameters

Level: \( N \) = \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(258048\)
Trace bound: \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1560))\).

Total New Old
Modular forms 66816 24916 41900
Cusp forms 62209 24388 37821
Eisenstein series 4607 528 4079

Trace form

\( 24388 q - 8 q^{2} - 28 q^{3} - 48 q^{4} - 8 q^{5} - 48 q^{6} - 64 q^{7} + 16 q^{8} - 48 q^{9} + O(q^{10}) \) \( 24388 q - 8 q^{2} - 28 q^{3} - 48 q^{4} - 8 q^{5} - 48 q^{6} - 64 q^{7} + 16 q^{8} - 48 q^{9} - 48 q^{10} + 40 q^{12} - 8 q^{13} + 64 q^{14} - 48 q^{16} - 12 q^{17} + 16 q^{18} - 16 q^{19} + 64 q^{20} - 16 q^{21} + 16 q^{22} - 8 q^{24} - 128 q^{25} + 16 q^{26} - 28 q^{27} - 48 q^{28} - 12 q^{29} - 28 q^{30} - 48 q^{31} - 48 q^{32} - 16 q^{33} - 80 q^{34} + 72 q^{35} - 56 q^{36} + 68 q^{37} - 80 q^{38} + 20 q^{39} - 176 q^{40} + 36 q^{41} + 56 q^{42} + 192 q^{43} + 128 q^{44} - 6 q^{45} + 208 q^{46} + 112 q^{47} + 24 q^{48} + 112 q^{50} - 24 q^{51} + 392 q^{52} + 112 q^{53} - 96 q^{54} + 104 q^{55} + 400 q^{56} - 24 q^{57} + 304 q^{58} + 96 q^{59} - 60 q^{60} + 84 q^{61} + 224 q^{62} - 80 q^{63} + 144 q^{64} + 34 q^{65} - 176 q^{66} - 48 q^{67} - 112 q^{68} + 72 q^{69} - 96 q^{70} - 32 q^{71} - 168 q^{72} + 64 q^{73} - 112 q^{74} - 24 q^{75} - 208 q^{76} - 96 q^{78} - 224 q^{79} - 160 q^{80} + 48 q^{81} - 304 q^{82} - 160 q^{83} - 336 q^{84} + 146 q^{85} - 160 q^{86} + 96 q^{87} - 192 q^{88} + 224 q^{89} - 264 q^{90} + 304 q^{91} - 272 q^{92} + 280 q^{93} - 176 q^{94} + 192 q^{95} - 280 q^{96} + 96 q^{97} - 232 q^{98} + 184 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1560))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1560.2.a \(\chi_{1560}(1, \cdot)\) 1560.2.a.a 1 1
1560.2.a.b 1
1560.2.a.c 1
1560.2.a.d 1
1560.2.a.e 1
1560.2.a.f 1
1560.2.a.g 1
1560.2.a.h 1
1560.2.a.i 1
1560.2.a.j 1
1560.2.a.k 1
1560.2.a.l 1
1560.2.a.m 2
1560.2.a.n 2
1560.2.a.o 2
1560.2.a.p 3
1560.2.a.q 3
1560.2.b \(\chi_{1560}(469, \cdot)\) n/a 144 1
1560.2.e \(\chi_{1560}(131, \cdot)\) n/a 192 1
1560.2.g \(\chi_{1560}(961, \cdot)\) 1560.2.g.a 2 1
1560.2.g.b 2
1560.2.g.c 2
1560.2.g.d 2
1560.2.g.e 2
1560.2.g.f 4
1560.2.g.g 4
1560.2.g.h 4
1560.2.g.i 6
1560.2.h \(\chi_{1560}(1559, \cdot)\) None 0 1
1560.2.k \(\chi_{1560}(911, \cdot)\) None 0 1
1560.2.l \(\chi_{1560}(1249, \cdot)\) 1560.2.l.a 2 1
1560.2.l.b 2
1560.2.l.c 6
1560.2.l.d 8
1560.2.l.e 8
1560.2.l.f 10
1560.2.n \(\chi_{1560}(779, \cdot)\) n/a 328 1
1560.2.q \(\chi_{1560}(181, \cdot)\) n/a 112 1
1560.2.r \(\chi_{1560}(649, \cdot)\) 1560.2.r.a 2 1
1560.2.r.b 2
1560.2.r.c 2
1560.2.r.d 2
1560.2.r.e 8
1560.2.r.f 8
1560.2.r.g 10
1560.2.r.h 10
1560.2.u \(\chi_{1560}(311, \cdot)\) None 0 1
1560.2.w \(\chi_{1560}(781, \cdot)\) 1560.2.w.a 2 1
1560.2.w.b 2
1560.2.w.c 4
1560.2.w.d 4
1560.2.w.e 16
1560.2.w.f 20
1560.2.w.g 22
1560.2.w.h 26
1560.2.x \(\chi_{1560}(1379, \cdot)\) n/a 288 1
1560.2.ba \(\chi_{1560}(1091, \cdot)\) n/a 224 1
1560.2.bb \(\chi_{1560}(1429, \cdot)\) n/a 168 1
1560.2.bd \(\chi_{1560}(599, \cdot)\) None 0 1
1560.2.bg \(\chi_{1560}(601, \cdot)\) 1560.2.bg.a 2 2
1560.2.bg.b 2
1560.2.bg.c 2
1560.2.bg.d 2
1560.2.bg.e 4
1560.2.bg.f 4
1560.2.bg.g 4
1560.2.bg.h 6
1560.2.bg.i 6
1560.2.bg.j 6
1560.2.bg.k 8
1560.2.bg.l 10
1560.2.bh \(\chi_{1560}(73, \cdot)\) 1560.2.bh.a 40 2
1560.2.bh.b 44
1560.2.bi \(\chi_{1560}(83, \cdot)\) n/a 656 2
1560.2.bn \(\chi_{1560}(853, \cdot)\) n/a 336 2
1560.2.bo \(\chi_{1560}(47, \cdot)\) None 0 2
1560.2.bq \(\chi_{1560}(77, \cdot)\) n/a 656 2
1560.2.br \(\chi_{1560}(833, \cdot)\) n/a 144 2
1560.2.bu \(\chi_{1560}(703, \cdot)\) None 0 2
1560.2.bv \(\chi_{1560}(883, \cdot)\) n/a 336 2
1560.2.by \(\chi_{1560}(1409, \cdot)\) n/a 168 2
1560.2.bz \(\chi_{1560}(629, \cdot)\) n/a 656 2
1560.2.cb \(\chi_{1560}(811, \cdot)\) n/a 224 2
1560.2.ce \(\chi_{1560}(31, \cdot)\) None 0 2
1560.2.cg \(\chi_{1560}(499, \cdot)\) n/a 336 2
1560.2.ch \(\chi_{1560}(1279, \cdot)\) None 0 2
1560.2.cj \(\chi_{1560}(161, \cdot)\) n/a 112 2
1560.2.cm \(\chi_{1560}(941, \cdot)\) n/a 448 2
1560.2.cn \(\chi_{1560}(103, \cdot)\) None 0 2
1560.2.cq \(\chi_{1560}(547, \cdot)\) n/a 288 2
1560.2.cr \(\chi_{1560}(53, \cdot)\) n/a 576 2
1560.2.cu \(\chi_{1560}(233, \cdot)\) n/a 168 2
1560.2.cx \(\chi_{1560}(203, \cdot)\) n/a 656 2
1560.2.cy \(\chi_{1560}(697, \cdot)\) 1560.2.cy.a 40 2
1560.2.cy.b 44
1560.2.cz \(\chi_{1560}(983, \cdot)\) None 0 2
1560.2.da \(\chi_{1560}(733, \cdot)\) n/a 336 2
1560.2.df \(\chi_{1560}(1199, \cdot)\) None 0 2
1560.2.dh \(\chi_{1560}(589, \cdot)\) n/a 336 2
1560.2.di \(\chi_{1560}(251, \cdot)\) n/a 448 2
1560.2.dl \(\chi_{1560}(419, \cdot)\) n/a 656 2
1560.2.dm \(\chi_{1560}(61, \cdot)\) n/a 224 2
1560.2.do \(\chi_{1560}(1031, \cdot)\) None 0 2
1560.2.dr \(\chi_{1560}(49, \cdot)\) 1560.2.dr.a 44 2
1560.2.dr.b 44
1560.2.ds \(\chi_{1560}(901, \cdot)\) n/a 224 2
1560.2.dv \(\chi_{1560}(179, \cdot)\) n/a 656 2
1560.2.dx \(\chi_{1560}(289, \cdot)\) 1560.2.dx.a 40 2
1560.2.dx.b 40
1560.2.dy \(\chi_{1560}(191, \cdot)\) None 0 2
1560.2.eb \(\chi_{1560}(719, \cdot)\) None 0 2
1560.2.ec \(\chi_{1560}(121, \cdot)\) 1560.2.ec.a 8 2
1560.2.ec.b 8
1560.2.ec.c 8
1560.2.ec.d 16
1560.2.ec.e 16
1560.2.ee \(\chi_{1560}(731, \cdot)\) n/a 448 2
1560.2.eh \(\chi_{1560}(1069, \cdot)\) n/a 336 2
1560.2.ek \(\chi_{1560}(1007, \cdot)\) None 0 4
1560.2.el \(\chi_{1560}(37, \cdot)\) n/a 672 4
1560.2.em \(\chi_{1560}(227, \cdot)\) n/a 1312 4
1560.2.en \(\chi_{1560}(817, \cdot)\) n/a 168 4
1560.2.eq \(\chi_{1560}(17, \cdot)\) n/a 336 4
1560.2.et \(\chi_{1560}(653, \cdot)\) n/a 1312 4
1560.2.eu \(\chi_{1560}(523, \cdot)\) n/a 672 4
1560.2.ex \(\chi_{1560}(127, \cdot)\) None 0 4
1560.2.ez \(\chi_{1560}(461, \cdot)\) n/a 896 4
1560.2.fa \(\chi_{1560}(41, \cdot)\) n/a 224 4
1560.2.fc \(\chi_{1560}(319, \cdot)\) None 0 4
1560.2.ff \(\chi_{1560}(19, \cdot)\) n/a 672 4
1560.2.fh \(\chi_{1560}(271, \cdot)\) None 0 4
1560.2.fi \(\chi_{1560}(331, \cdot)\) n/a 448 4
1560.2.fk \(\chi_{1560}(149, \cdot)\) n/a 1312 4
1560.2.fn \(\chi_{1560}(89, \cdot)\) n/a 336 4
1560.2.fp \(\chi_{1560}(43, \cdot)\) n/a 672 4
1560.2.fq \(\chi_{1560}(367, \cdot)\) None 0 4
1560.2.ft \(\chi_{1560}(113, \cdot)\) n/a 336 4
1560.2.fu \(\chi_{1560}(173, \cdot)\) n/a 1312 4
1560.2.fw \(\chi_{1560}(877, \cdot)\) n/a 672 4
1560.2.fx \(\chi_{1560}(167, \cdot)\) None 0 4
1560.2.gc \(\chi_{1560}(97, \cdot)\) n/a 168 4
1560.2.gd \(\chi_{1560}(947, \cdot)\) n/a 1312 4

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1560))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1560)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(260))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(312))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(390))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(520))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(780))\)\(^{\oplus 2}\)