## Defining parameters

 Level: $$N$$ = $$572 = 2^{2} \cdot 11 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Newform subspaces: $$37$$ Sturm bound: $$40320$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(572))$$.

Total New Old
Modular forms 10680 5908 4772
Cusp forms 9481 5516 3965
Eisenstein series 1199 392 807

## Trace form

 $$5516q - 38q^{2} - 38q^{4} - 76q^{5} - 38q^{6} + 14q^{7} - 38q^{8} - 40q^{9} + O(q^{10})$$ $$5516q - 38q^{2} - 38q^{4} - 76q^{5} - 38q^{6} + 14q^{7} - 38q^{8} - 40q^{9} - 48q^{10} + 16q^{11} - 100q^{12} - 57q^{13} - 96q^{14} + 24q^{15} - 78q^{16} - 80q^{17} - 124q^{18} - 38q^{19} - 136q^{20} - 180q^{21} - 134q^{22} - 34q^{23} - 194q^{24} - 150q^{25} - 128q^{26} - 72q^{27} - 148q^{28} - 72q^{29} - 144q^{30} + 4q^{31} - 108q^{32} - 74q^{33} - 96q^{34} + 66q^{35} + 12q^{36} - 114q^{37} + 35q^{39} + 32q^{40} - 124q^{41} + 88q^{42} + 16q^{43} + 56q^{44} - 306q^{45} + 132q^{46} + 22q^{47} + 168q^{48} - 210q^{49} + 66q^{50} - 10q^{51} + 70q^{52} - 310q^{53} + 36q^{54} - 26q^{55} - 40q^{56} - 238q^{57} - 12q^{58} - 28q^{59} - 68q^{60} - 132q^{61} - 164q^{62} + 4q^{63} - 170q^{64} - 196q^{65} - 264q^{66} - 38q^{67} - 324q^{68} - 134q^{69} - 172q^{70} - 112q^{71} - 294q^{72} - 122q^{73} - 296q^{74} - 22q^{75} - 168q^{76} - 142q^{77} - 316q^{78} + 14q^{79} - 236q^{80} - 78q^{81} - 98q^{82} - 34q^{83} - 112q^{84} + 36q^{85} - 46q^{86} + 76q^{87} + 74q^{88} - 86q^{89} + 40q^{90} + 39q^{91} - 144q^{92} + 12q^{93} + 36q^{94} + 50q^{95} + 132q^{96} + 56q^{97} - 24q^{98} + 34q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(572))$$

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
572.2.a $$\chi_{572}(1, \cdot)$$ 572.2.a.a 1 1
572.2.a.b 2
572.2.a.c 2
572.2.a.d 2
572.2.a.e 3
572.2.b $$\chi_{572}(571, \cdot)$$ 572.2.b.a 4 1
572.2.b.b 20
572.2.b.c 56
572.2.e $$\chi_{572}(131, \cdot)$$ 572.2.e.a 8 1
572.2.e.b 64
572.2.f $$\chi_{572}(441, \cdot)$$ 572.2.f.a 2 1
572.2.f.b 4
572.2.f.c 8
572.2.i $$\chi_{572}(133, \cdot)$$ 572.2.i.a 4 2
572.2.i.b 6
572.2.i.c 10
572.2.j $$\chi_{572}(463, \cdot)$$ 572.2.j.a 140 2
572.2.m $$\chi_{572}(21, \cdot)$$ 572.2.m.a 28 2
572.2.n $$\chi_{572}(53, \cdot)$$ 572.2.n.a 20 4
572.2.n.b 28
572.2.p $$\chi_{572}(309, \cdot)$$ 572.2.p.a 24 2
572.2.s $$\chi_{572}(43, \cdot)$$ 572.2.s.a 160 2
572.2.t $$\chi_{572}(87, \cdot)$$ 572.2.t.a 160 2
572.2.x $$\chi_{572}(25, \cdot)$$ 572.2.x.a 56 4
572.2.y $$\chi_{572}(79, \cdot)$$ 572.2.y.a 288 4
572.2.bb $$\chi_{572}(51, \cdot)$$ 572.2.bb.a 16 4
572.2.bb.b 304
572.2.bc $$\chi_{572}(197, \cdot)$$ 572.2.bc.a 56 4
572.2.bf $$\chi_{572}(67, \cdot)$$ 572.2.bf.a 280 4
572.2.bg $$\chi_{572}(9, \cdot)$$ 572.2.bg.a 112 8
572.2.bh $$\chi_{572}(57, \cdot)$$ 572.2.bh.a 112 8
572.2.bk $$\chi_{572}(31, \cdot)$$ 572.2.bk.a 640 8
572.2.bm $$\chi_{572}(35, \cdot)$$ 572.2.bm.a 640 8
572.2.bn $$\chi_{572}(95, \cdot)$$ 572.2.bn.a 640 8
572.2.bq $$\chi_{572}(49, \cdot)$$ 572.2.bq.a 112 8
572.2.bs $$\chi_{572}(15, \cdot)$$ 572.2.bs.a 1280 16
572.2.bv $$\chi_{572}(41, \cdot)$$ 572.2.bv.a 224 16

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(572))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(572)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(143))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(286))$$$$^{\oplus 2}$$