# Properties

 Label 1716.2 Level 1716 Weight 2 Dimension 33880 Nonzero newspaces 48 Sturm bound 322560 Trace bound 17

## Defining parameters

 Level: $$N$$ = $$1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$322560$$ Trace bound: $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1716))$$.

Total New Old
Modular forms 83040 34680 48360
Cusp forms 78241 33880 44361
Eisenstein series 4799 800 3999

## Trace form

 $$33880q - 76q^{4} - 38q^{6} - 28q^{7} - 100q^{9} + O(q^{10})$$ $$33880q - 76q^{4} - 38q^{6} - 28q^{7} - 100q^{9} - 56q^{10} - 32q^{11} - 76q^{12} - 230q^{13} + 20q^{14} - 24q^{15} + 4q^{16} + 8q^{17} + 18q^{18} + 76q^{19} + 196q^{20} + 28q^{21} + 92q^{22} + 88q^{23} + 118q^{24} + 36q^{25} + 170q^{26} + 102q^{27} + 144q^{28} + 100q^{29} + 68q^{30} + 88q^{31} + 120q^{32} + 34q^{33} - 160q^{34} + 88q^{35} - 82q^{36} + 20q^{37} - 100q^{38} + 91q^{39} - 408q^{40} + 252q^{41} - 204q^{42} + 64q^{43} - 200q^{44} + 70q^{45} - 416q^{46} + 28q^{47} - 244q^{48} + 172q^{49} - 356q^{50} + 38q^{51} - 352q^{52} + 196q^{53} - 164q^{54} - 28q^{55} - 296q^{56} - 74q^{57} - 288q^{58} - 84q^{59} - 408q^{60} - 120q^{61} - 120q^{62} - 254q^{63} - 196q^{64} - 24q^{65} - 312q^{66} - 180q^{67} - 322q^{69} - 336q^{70} - 128q^{71} - 364q^{72} - 332q^{73} - 100q^{74} - 358q^{75} - 216q^{76} - 172q^{77} - 436q^{78} - 204q^{79} - 220q^{80} - 300q^{81} - 276q^{82} - 132q^{83} - 440q^{84} - 408q^{85} - 256q^{86} - 168q^{87} - 468q^{88} - 224q^{89} - 308q^{90} - 54q^{91} - 204q^{92} - 208q^{93} - 368q^{94} - 36q^{95} - 220q^{96} - 200q^{97} - 216q^{98} + 198q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1716))$$

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
1716.2.a $$\chi_{1716}(1, \cdot)$$ 1716.2.a.a 1 1
1716.2.a.b 1
1716.2.a.c 1
1716.2.a.d 2
1716.2.a.e 2
1716.2.a.f 3
1716.2.a.g 3
1716.2.a.h 3
1716.2.a.i 4
1716.2.b $$\chi_{1716}(571, \cdot)$$ n/a 168 1
1716.2.c $$\chi_{1716}(287, \cdot)$$ n/a 240 1
1716.2.d $$\chi_{1716}(989, \cdot)$$ 1716.2.d.a 48 1
1716.2.e $$\chi_{1716}(1585, \cdot)$$ 1716.2.e.a 10 1
1716.2.e.b 10
1716.2.n $$\chi_{1716}(703, \cdot)$$ n/a 144 1
1716.2.o $$\chi_{1716}(155, \cdot)$$ n/a 280 1
1716.2.p $$\chi_{1716}(857, \cdot)$$ 1716.2.p.a 56 1
1716.2.q $$\chi_{1716}(133, \cdot)$$ 1716.2.q.a 2 2
1716.2.q.b 12
1716.2.q.c 12
1716.2.q.d 12
1716.2.q.e 14
1716.2.r $$\chi_{1716}(395, \cdot)$$ n/a 656 2
1716.2.t $$\chi_{1716}(463, \cdot)$$ n/a 280 2
1716.2.v $$\chi_{1716}(109, \cdot)$$ 1716.2.v.a 4 2
1716.2.v.b 4
1716.2.v.c 20
1716.2.v.d 28
1716.2.x $$\chi_{1716}(749, \cdot)$$ 1716.2.x.a 96 2
1716.2.z $$\chi_{1716}(157, \cdot)$$ 1716.2.z.a 4 4
1716.2.z.b 4
1716.2.z.c 4
1716.2.z.d 16
1716.2.z.e 20
1716.2.z.f 20
1716.2.z.g 28
1716.2.be $$\chi_{1716}(1057, \cdot)$$ 1716.2.be.a 20 2
1716.2.be.b 24
1716.2.bf $$\chi_{1716}(1121, \cdot)$$ n/a 112 2
1716.2.bg $$\chi_{1716}(419, \cdot)$$ n/a 560 2
1716.2.bh $$\chi_{1716}(43, \cdot)$$ n/a 336 2
1716.2.bi $$\chi_{1716}(329, \cdot)$$ n/a 112 2
1716.2.bj $$\chi_{1716}(23, \cdot)$$ n/a 560 2
1716.2.bk $$\chi_{1716}(835, \cdot)$$ n/a 336 2
1716.2.bp $$\chi_{1716}(233, \cdot)$$ n/a 224 4
1716.2.bq $$\chi_{1716}(79, \cdot)$$ n/a 576 4
1716.2.br $$\chi_{1716}(311, \cdot)$$ n/a 1312 4
1716.2.ca $$\chi_{1716}(365, \cdot)$$ n/a 192 4
1716.2.cb $$\chi_{1716}(25, \cdot)$$ n/a 112 4
1716.2.cc $$\chi_{1716}(259, \cdot)$$ n/a 672 4
1716.2.cd $$\chi_{1716}(443, \cdot)$$ n/a 1152 4
1716.2.cf $$\chi_{1716}(89, \cdot)$$ n/a 184 4
1716.2.ch $$\chi_{1716}(241, \cdot)$$ n/a 112 4
1716.2.cj $$\chi_{1716}(67, \cdot)$$ n/a 560 4
1716.2.cl $$\chi_{1716}(527, \cdot)$$ n/a 1312 4
1716.2.cm $$\chi_{1716}(289, \cdot)$$ n/a 224 8
1716.2.co $$\chi_{1716}(73, \cdot)$$ n/a 224 8
1716.2.cq $$\chi_{1716}(5, \cdot)$$ n/a 448 8
1716.2.cs $$\chi_{1716}(83, \cdot)$$ n/a 2624 8
1716.2.cu $$\chi_{1716}(31, \cdot)$$ n/a 1344 8
1716.2.cz $$\chi_{1716}(179, \cdot)$$ n/a 2624 8
1716.2.da $$\chi_{1716}(139, \cdot)$$ n/a 1344 8
1716.2.db $$\chi_{1716}(17, \cdot)$$ n/a 448 8
1716.2.dc $$\chi_{1716}(191, \cdot)$$ n/a 2624 8
1716.2.dd $$\chi_{1716}(127, \cdot)$$ n/a 1344 8
1716.2.de $$\chi_{1716}(49, \cdot)$$ n/a 224 8
1716.2.df $$\chi_{1716}(29, \cdot)$$ n/a 448 8
1716.2.dk $$\chi_{1716}(115, \cdot)$$ n/a 2688 16
1716.2.dm $$\chi_{1716}(167, \cdot)$$ n/a 5248 16
1716.2.do $$\chi_{1716}(137, \cdot)$$ n/a 896 16
1716.2.dq $$\chi_{1716}(85, \cdot)$$ n/a 448 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1716))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1716)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(132))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(143))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(156))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(286))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(429))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(572))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(858))$$$$^{\oplus 2}$$