Properties

Label 1710.2
Level 1710
Weight 2
Dimension 18704
Nonzero newspaces 48
Sturm bound 311040
Trace bound 17

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Defining parameters

Level: \( N \) = \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(311040\)
Trace bound: \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1710))\).

Total New Old
Modular forms 80064 18704 61360
Cusp forms 75457 18704 56753
Eisenstein series 4607 0 4607

Trace form

\( 18704q - 6q^{2} - 12q^{3} - 6q^{4} - 10q^{5} + 12q^{6} - 24q^{7} + 6q^{8} + 28q^{9} + O(q^{10}) \) \( 18704q - 6q^{2} - 12q^{3} - 6q^{4} - 10q^{5} + 12q^{6} - 24q^{7} + 6q^{8} + 28q^{9} + 22q^{10} + 52q^{11} + 16q^{12} - 20q^{13} + 4q^{14} + 48q^{15} - 6q^{16} + 8q^{18} - 76q^{19} + 4q^{20} + 72q^{21} - 34q^{22} + 36q^{23} - 12q^{24} - 2q^{25} - 48q^{26} + 48q^{27} - 12q^{28} - 24q^{29} - 20q^{31} - 6q^{32} - 20q^{33} - 8q^{34} - 68q^{35} - 20q^{36} + 16q^{37} - 42q^{38} - 128q^{39} + 6q^{40} - 188q^{41} - 128q^{42} - 56q^{43} - 10q^{44} - 52q^{45} + 216q^{46} + 168q^{47} + 16q^{48} + 210q^{49} + 122q^{50} + 300q^{51} + 16q^{52} + 372q^{53} + 156q^{54} + 256q^{55} + 176q^{56} + 334q^{57} + 148q^{58} + 520q^{59} + 88q^{60} + 392q^{61} + 324q^{62} + 368q^{63} + 42q^{64} + 336q^{65} + 384q^{66} + 216q^{67} + 126q^{68} + 344q^{69} + 156q^{70} + 432q^{71} + 48q^{72} + 98q^{73} + 100q^{74} - 12q^{75} + 46q^{76} + 24q^{77} + 56q^{78} + 52q^{79} - 10q^{80} - 4q^{81} + 188q^{82} + 24q^{84} + 276q^{85} + 212q^{86} + 40q^{87} + 20q^{88} + 164q^{89} + 112q^{90} + 224q^{91} + 144q^{92} - 64q^{93} + 200q^{94} + 258q^{95} + 16q^{96} + 412q^{97} + 198q^{98} + 292q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1710))\)

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
1710.2.a \(\chi_{1710}(1, \cdot)\) 1710.2.a.a 1 1
1710.2.a.b 1
1710.2.a.c 1
1710.2.a.d 1
1710.2.a.e 1
1710.2.a.f 1
1710.2.a.g 1
1710.2.a.h 1
1710.2.a.i 1
1710.2.a.j 1
1710.2.a.k 1
1710.2.a.l 1
1710.2.a.m 1
1710.2.a.n 1
1710.2.a.o 1
1710.2.a.p 1
1710.2.a.q 1
1710.2.a.r 1
1710.2.a.s 1
1710.2.a.t 1
1710.2.a.u 2
1710.2.a.v 2
1710.2.a.w 2
1710.2.a.x 2
1710.2.a.y 2
1710.2.c \(\chi_{1710}(1709, \cdot)\) 1710.2.c.a 4 1
1710.2.c.b 4
1710.2.c.c 8
1710.2.c.d 24
1710.2.d \(\chi_{1710}(1369, \cdot)\) 1710.2.d.a 2 1
1710.2.d.b 2
1710.2.d.c 4
1710.2.d.d 6
1710.2.d.e 6
1710.2.d.f 6
1710.2.d.g 8
1710.2.d.h 12
1710.2.f \(\chi_{1710}(341, \cdot)\) 1710.2.f.a 16 1
1710.2.f.b 16
1710.2.i \(\chi_{1710}(121, \cdot)\) n/a 160 2
1710.2.j \(\chi_{1710}(571, \cdot)\) n/a 144 2
1710.2.k \(\chi_{1710}(391, \cdot)\) n/a 160 2
1710.2.l \(\chi_{1710}(1261, \cdot)\) 1710.2.l.a 2 2
1710.2.l.b 2
1710.2.l.c 2
1710.2.l.d 2
1710.2.l.e 2
1710.2.l.f 2
1710.2.l.g 2
1710.2.l.h 2
1710.2.l.i 2
1710.2.l.j 4
1710.2.l.k 4
1710.2.l.l 4
1710.2.l.m 4
1710.2.l.n 4
1710.2.l.o 6
1710.2.l.p 6
1710.2.l.q 6
1710.2.l.r 8
1710.2.l.s 8
1710.2.n \(\chi_{1710}(647, \cdot)\) 1710.2.n.a 4 2
1710.2.n.b 4
1710.2.n.c 4
1710.2.n.d 4
1710.2.n.e 4
1710.2.n.f 8
1710.2.n.g 8
1710.2.n.h 16
1710.2.n.i 20
1710.2.p \(\chi_{1710}(37, \cdot)\) 1710.2.p.a 4 2
1710.2.p.b 16
1710.2.p.c 20
1710.2.p.d 20
1710.2.p.e 40
1710.2.q \(\chi_{1710}(179, \cdot)\) 1710.2.q.a 16 2
1710.2.q.b 64
1710.2.t \(\chi_{1710}(919, \cdot)\) 1710.2.t.a 8 2
1710.2.t.b 12
1710.2.t.c 20
1710.2.t.d 20
1710.2.t.e 40
1710.2.x \(\chi_{1710}(1361, \cdot)\) n/a 160 2
1710.2.ba \(\chi_{1710}(911, \cdot)\) n/a 160 2
1710.2.bb \(\chi_{1710}(221, \cdot)\) n/a 160 2
1710.2.bd \(\chi_{1710}(49, \cdot)\) n/a 240 2
1710.2.bg \(\chi_{1710}(229, \cdot)\) n/a 216 2
1710.2.bh \(\chi_{1710}(619, \cdot)\) n/a 240 2
1710.2.bk \(\chi_{1710}(749, \cdot)\) n/a 240 2
1710.2.bl \(\chi_{1710}(569, \cdot)\) n/a 240 2
1710.2.bo \(\chi_{1710}(1019, \cdot)\) n/a 240 2
1710.2.bq \(\chi_{1710}(521, \cdot)\) 1710.2.bq.a 32 2
1710.2.bq.b 32
1710.2.bs \(\chi_{1710}(271, \cdot)\) n/a 192 6
1710.2.bt \(\chi_{1710}(61, \cdot)\) n/a 480 6
1710.2.bu \(\chi_{1710}(481, \cdot)\) n/a 480 6
1710.2.bv \(\chi_{1710}(197, \cdot)\) n/a 160 4
1710.2.by \(\chi_{1710}(493, \cdot)\) n/a 480 4
1710.2.bz \(\chi_{1710}(103, \cdot)\) n/a 480 4
1710.2.cc \(\chi_{1710}(373, \cdot)\) n/a 480 4
1710.2.ce \(\chi_{1710}(77, \cdot)\) n/a 432 4
1710.2.cf \(\chi_{1710}(83, \cdot)\) n/a 480 4
1710.2.ci \(\chi_{1710}(353, \cdot)\) n/a 480 4
1710.2.cj \(\chi_{1710}(217, \cdot)\) n/a 200 4
1710.2.cl \(\chi_{1710}(139, \cdot)\) n/a 720 6
1710.2.co \(\chi_{1710}(299, \cdot)\) n/a 720 6
1710.2.cp \(\chi_{1710}(41, \cdot)\) n/a 480 6
1710.2.ct \(\chi_{1710}(71, \cdot)\) n/a 144 6
1710.2.cv \(\chi_{1710}(29, \cdot)\) n/a 720 6
1710.2.cx \(\chi_{1710}(199, \cdot)\) n/a 300 6
1710.2.da \(\chi_{1710}(89, \cdot)\) n/a 240 6
1710.2.dc \(\chi_{1710}(499, \cdot)\) n/a 720 6
1710.2.df \(\chi_{1710}(641, \cdot)\) n/a 480 6
1710.2.dh \(\chi_{1710}(47, \cdot)\) n/a 1440 12
1710.2.dk \(\chi_{1710}(13, \cdot)\) n/a 1440 12
1710.2.dl \(\chi_{1710}(127, \cdot)\) n/a 600 12
1710.2.dm \(\chi_{1710}(23, \cdot)\) n/a 1440 12
1710.2.dn \(\chi_{1710}(17, \cdot)\) n/a 480 12
1710.2.dq \(\chi_{1710}(193, \cdot)\) n/a 1440 12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1710))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1710)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(285))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(342))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(570))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(855))\)\(^{\oplus 2}\)