# Properties

 Label 574.2 Level 574 Weight 2 Dimension 3219 Nonzero newspaces 16 Newforms 61 Sturm bound 40320 Trace bound 5

## Defining parameters

 Level: $$N$$ = $$574 = 2 \cdot 7 \cdot 41$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Newforms: $$61$$ Sturm bound: $$40320$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(574))$$.

Total New Old
Modular forms 10560 3219 7341
Cusp forms 9601 3219 6382
Eisenstein series 959 0 959

## Trace form

 $$3219q + 3q^{2} + 8q^{3} - q^{4} + 6q^{5} - q^{7} + 3q^{8} + 11q^{9} + O(q^{10})$$ $$3219q + 3q^{2} + 8q^{3} - q^{4} + 6q^{5} - q^{7} + 3q^{8} + 11q^{9} + 6q^{10} + 12q^{11} + 8q^{12} + 22q^{13} + 3q^{14} + 24q^{15} - q^{16} + 6q^{17} + 15q^{18} + 16q^{19} + 6q^{20} + 8q^{21} + 12q^{22} + 24q^{23} + 41q^{25} + 6q^{26} + 32q^{27} - q^{28} + 42q^{29} - 56q^{30} - 40q^{31} - 17q^{32} - 192q^{33} - 70q^{34} - 74q^{35} - 29q^{36} - 206q^{37} - 56q^{38} - 280q^{39} - 74q^{40} - 45q^{41} - 160q^{42} - 52q^{43} - 68q^{44} - 242q^{45} - 56q^{46} - 168q^{47} - 32q^{48} - 81q^{49} - 79q^{50} - 144q^{51} + 2q^{52} - 38q^{53} - 32q^{54} + 72q^{55} + 3q^{56} + 88q^{57} + 18q^{58} + 72q^{59} + 24q^{60} + 46q^{61} + 24q^{62} + 11q^{63} - q^{64} + 64q^{65} + 48q^{66} - 44q^{67} + 6q^{68} - 64q^{69} + 6q^{70} - 88q^{71} + 15q^{72} - 90q^{73} + 42q^{74} - 216q^{75} + 16q^{76} - 68q^{77} + 72q^{78} - 96q^{79} + 6q^{80} - 197q^{81} + 47q^{82} - 64q^{83} + 8q^{84} - 232q^{85} + 60q^{86} - 64q^{87} + 12q^{88} - 58q^{89} + 78q^{90} - 138q^{91} + 24q^{92} - 48q^{93} + 24q^{94} - 40q^{95} - 42q^{97} + 3q^{98} + 36q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(574))$$

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
574.2.a $$\chi_{574}(1, \cdot)$$ 574.2.a.a 1 1
574.2.a.b 1
574.2.a.c 1
574.2.a.d 1
574.2.a.e 1
574.2.a.f 1
574.2.a.g 1
574.2.a.h 1
574.2.a.i 1
574.2.a.j 1
574.2.a.k 2
574.2.a.l 3
574.2.a.m 4
574.2.c $$\chi_{574}(491, \cdot)$$ 574.2.c.a 2 1
574.2.c.b 8
574.2.c.c 10
574.2.e $$\chi_{574}(165, \cdot)$$ 574.2.e.a 2 2
574.2.e.b 2
574.2.e.c 2
574.2.e.d 4
574.2.e.e 6
574.2.e.f 8
574.2.e.g 12
574.2.e.h 20
574.2.f $$\chi_{574}(155, \cdot)$$ 574.2.f.a 20 2
574.2.f.b 24
574.2.h $$\chi_{574}(57, \cdot)$$ 574.2.h.a 4 4
574.2.h.b 4
574.2.h.c 4
574.2.h.d 4
574.2.h.e 4
574.2.h.f 4
574.2.h.g 8
574.2.h.h 8
574.2.h.i 8
574.2.h.j 12
574.2.h.k 20
574.2.j $$\chi_{574}(81, \cdot)$$ 574.2.j.a 28 2
574.2.j.b 28
574.2.m $$\chi_{574}(27, \cdot)$$ 574.2.m.a 56 4
574.2.m.b 56
574.2.n $$\chi_{574}(113, \cdot)$$ 574.2.n.a 40 4
574.2.n.b 40
574.2.r $$\chi_{574}(9, \cdot)$$ 574.2.r.a 8 4
574.2.r.b 8
574.2.r.c 40
574.2.r.d 56
574.2.s $$\chi_{574}(37, \cdot)$$ 574.2.s.a 112 8
574.2.s.b 112
574.2.u $$\chi_{574}(43, \cdot)$$ 574.2.u.a 80 8
574.2.u.b 96
574.2.v $$\chi_{574}(3, \cdot)$$ 574.2.v.a 112 8
574.2.v.b 112
574.2.z $$\chi_{574}(23, \cdot)$$ 574.2.z.a 112 8
574.2.z.b 112
574.2.ba $$\chi_{574}(13, \cdot)$$ 574.2.ba.a 224 16
574.2.ba.b 224
574.2.bc $$\chi_{574}(39, \cdot)$$ 574.2.bc.a 224 16
574.2.bc.b 224
574.2.bf $$\chi_{574}(17, \cdot)$$ 574.2.bf.a 448 32
574.2.bf.b 448

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(574))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(574)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(41))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(82))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(287))$$$$^{\oplus 2}$$