# Properties

 Label 580.2 Level 580 Weight 2 Dimension 5216 Nonzero newspaces 20 Newform subspaces 50 Sturm bound 40320 Trace bound 9

## Defining parameters

 Level: $$N$$ = $$580 = 2^{2} \cdot 5 \cdot 29$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$20$$ Newform subspaces: $$50$$ Sturm bound: $$40320$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(580))$$.

Total New Old
Modular forms 10640 5536 5104
Cusp forms 9521 5216 4305
Eisenstein series 1119 320 799

## Trace form

 $$5216 q - 24 q^{2} + 4 q^{3} - 28 q^{4} - 74 q^{5} - 84 q^{6} - 4 q^{7} - 36 q^{8} - 58 q^{9} + O(q^{10})$$ $$5216 q - 24 q^{2} + 4 q^{3} - 28 q^{4} - 74 q^{5} - 84 q^{6} - 4 q^{7} - 36 q^{8} - 58 q^{9} - 54 q^{10} - 28 q^{12} - 56 q^{13} - 28 q^{14} - 4 q^{15} - 68 q^{16} - 56 q^{17} - 16 q^{18} + 8 q^{19} - 34 q^{20} - 104 q^{21} - 28 q^{22} + 16 q^{23} - 28 q^{24} - 70 q^{25} - 92 q^{26} + 76 q^{27} - 56 q^{28} - 6 q^{29} - 84 q^{30} + 64 q^{31} - 44 q^{32} + 28 q^{33} - 28 q^{34} + 32 q^{35} - 108 q^{36} - 4 q^{37} - 28 q^{38} + 64 q^{39} - 34 q^{40} - 148 q^{41} - 28 q^{42} + 20 q^{43} - 56 q^{44} - 129 q^{45} - 224 q^{46} - 44 q^{47} - 252 q^{48} - 162 q^{49} - 112 q^{50} - 136 q^{51} - 244 q^{52} - 206 q^{53} - 280 q^{54} - 112 q^{55} - 280 q^{56} - 240 q^{57} - 372 q^{58} - 80 q^{59} - 210 q^{60} - 332 q^{61} - 224 q^{62} - 228 q^{63} - 280 q^{64} - 147 q^{65} - 308 q^{66} - 116 q^{67} - 200 q^{68} - 144 q^{69} - 154 q^{70} + 52 q^{71} - 144 q^{72} - 30 q^{73} - 56 q^{74} + 74 q^{75} - 84 q^{76} + 84 q^{77} - 28 q^{78} + 40 q^{79} - 74 q^{80} + 114 q^{81} - 60 q^{82} + 100 q^{83} + 56 q^{84} + 24 q^{85} - 112 q^{86} + 152 q^{87} - 56 q^{88} + 96 q^{89} - 96 q^{90} + 160 q^{91} - 28 q^{92} + 40 q^{93} - 28 q^{94} + 104 q^{95} - 210 q^{97} + 84 q^{98} + 28 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(580))$$

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
580.2.a $$\chi_{580}(1, \cdot)$$ 580.2.a.a 1 1
580.2.a.b 1
580.2.a.c 3
580.2.a.d 3
580.2.c $$\chi_{580}(349, \cdot)$$ 580.2.c.a 4 1
580.2.c.b 10
580.2.d $$\chi_{580}(521, \cdot)$$ 580.2.d.a 2 1
580.2.d.b 4
580.2.d.c 4
580.2.f $$\chi_{580}(289, \cdot)$$ 580.2.f.a 16 1
580.2.j $$\chi_{580}(17, \cdot)$$ 580.2.j.a 30 2
580.2.k $$\chi_{580}(191, \cdot)$$ 580.2.k.a 60 2
580.2.k.b 60
580.2.n $$\chi_{580}(407, \cdot)$$ 580.2.n.a 2 2
580.2.n.b 2
580.2.n.c 8
580.2.n.d 76
580.2.n.e 80
580.2.o $$\chi_{580}(347, \cdot)$$ 580.2.o.a 2 2
580.2.o.b 2
580.2.o.c 12
580.2.o.d 12
580.2.o.e 144
580.2.r $$\chi_{580}(99, \cdot)$$ 580.2.r.a 2 2
580.2.r.b 2
580.2.r.c 4
580.2.r.d 4
580.2.r.e 160
580.2.s $$\chi_{580}(133, \cdot)$$ 580.2.s.a 30 2
580.2.u $$\chi_{580}(81, \cdot)$$ 580.2.u.a 24 6
580.2.u.b 36
580.2.x $$\chi_{580}(9, \cdot)$$ 580.2.x.a 96 6
580.2.z $$\chi_{580}(121, \cdot)$$ 580.2.z.a 24 6
580.2.z.b 36
580.2.ba $$\chi_{580}(49, \cdot)$$ 580.2.ba.a 84 6
580.2.bc $$\chi_{580}(37, \cdot)$$ 580.2.bc.a 180 12
580.2.be $$\chi_{580}(19, \cdot)$$ 580.2.be.a 12 12
580.2.be.b 12
580.2.be.c 24
580.2.be.d 24
580.2.be.e 960
580.2.bh $$\chi_{580}(63, \cdot)$$ 580.2.bh.a 12 12
580.2.bh.b 12
580.2.bh.c 1008
580.2.bi $$\chi_{580}(7, \cdot)$$ 580.2.bi.a 12 12
580.2.bi.b 12
580.2.bi.c 1008
580.2.bl $$\chi_{580}(11, \cdot)$$ 580.2.bl.a 360 12
580.2.bl.b 360
580.2.bn $$\chi_{580}(73, \cdot)$$ 580.2.bn.a 180 12

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(580))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(580)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(58))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(116))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(145))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(290))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(580))$$$$^{\oplus 1}$$