# Properties

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

## 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

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

## 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 available 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

$$S_{2}^{\mathrm{old}}(\Gamma_1(1710)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(171))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(190))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(285))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(342))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(570))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(855))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1710))$$$$^{\oplus 1}$$