# Properties

 Label 440.2 Level 440 Weight 2 Dimension 2812 Nonzero newspaces 18 Newform subspaces 50 Sturm bound 23040 Trace bound 6

## Defining parameters

 Level: $$N$$ = $$440 = 2^{3} \cdot 5 \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$18$$ Newform subspaces: $$50$$ Sturm bound: $$23040$$ Trace bound: $$6$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(440))$$.

Total New Old
Modular forms 6240 3028 3212
Cusp forms 5281 2812 2469
Eisenstein series 959 216 743

## Trace form

 $$2812 q - 12 q^{2} - 12 q^{3} - 12 q^{4} + 2 q^{5} - 44 q^{6} - 4 q^{7} - 12 q^{8} - 14 q^{9} + O(q^{10})$$ $$2812 q - 12 q^{2} - 12 q^{3} - 12 q^{4} + 2 q^{5} - 44 q^{6} - 4 q^{7} - 12 q^{8} - 14 q^{9} - 22 q^{10} - 48 q^{11} - 56 q^{12} + 4 q^{13} - 36 q^{14} - 28 q^{15} - 76 q^{16} - 8 q^{17} - 68 q^{18} - 14 q^{19} - 62 q^{20} + 24 q^{21} - 36 q^{22} - 20 q^{23} - 68 q^{24} - 14 q^{25} - 76 q^{26} - 6 q^{27} - 4 q^{28} + 32 q^{29} - 60 q^{30} - 40 q^{31} + 8 q^{32} - 62 q^{33} - 48 q^{34} - 76 q^{35} - 140 q^{36} - 12 q^{37} - 72 q^{38} - 156 q^{39} - 12 q^{40} - 144 q^{41} - 192 q^{42} - 140 q^{43} - 144 q^{44} - 28 q^{45} - 136 q^{46} - 128 q^{47} - 224 q^{48} - 114 q^{49} - 132 q^{50} - 186 q^{51} - 160 q^{52} + 28 q^{53} - 228 q^{54} - 68 q^{55} - 296 q^{56} - 22 q^{57} - 128 q^{58} + 10 q^{59} - 160 q^{60} + 84 q^{61} - 132 q^{62} + 16 q^{63} - 84 q^{64} - 48 q^{65} - 76 q^{66} + 80 q^{67} - 60 q^{68} + 64 q^{69} + 40 q^{70} + 28 q^{71} + 104 q^{72} - 112 q^{73} + 120 q^{74} + 52 q^{75} + 100 q^{76} + 36 q^{77} + 328 q^{78} - 20 q^{79} + 128 q^{80} - 176 q^{81} + 252 q^{82} - 90 q^{83} + 284 q^{84} - 64 q^{85} + 44 q^{86} - 144 q^{87} + 300 q^{88} - 168 q^{89} + 118 q^{90} - 288 q^{91} + 172 q^{92} - 180 q^{93} + 156 q^{94} - 166 q^{95} - 16 q^{96} - 162 q^{97} + 176 q^{98} - 316 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(440))$$

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
440.2.a $$\chi_{440}(1, \cdot)$$ 440.2.a.a 1 1
440.2.a.b 1
440.2.a.c 1
440.2.a.d 1
440.2.a.e 2
440.2.a.f 2
440.2.a.g 2
440.2.b $$\chi_{440}(89, \cdot)$$ 440.2.b.a 2 1
440.2.b.b 2
440.2.b.c 2
440.2.b.d 8
440.2.c $$\chi_{440}(219, \cdot)$$ 440.2.c.a 4 1
440.2.c.b 8
440.2.c.c 56
440.2.f $$\chi_{440}(351, \cdot)$$ None 0 1
440.2.g $$\chi_{440}(221, \cdot)$$ 440.2.g.a 4 1
440.2.g.b 12
440.2.g.c 24
440.2.l $$\chi_{440}(309, \cdot)$$ 440.2.l.a 2 1
440.2.l.b 2
440.2.l.c 56
440.2.m $$\chi_{440}(439, \cdot)$$ None 0 1
440.2.p $$\chi_{440}(131, \cdot)$$ 440.2.p.a 48 1
440.2.r $$\chi_{440}(67, \cdot)$$ 440.2.r.a 2 2
440.2.r.b 2
440.2.r.c 2
440.2.r.d 2
440.2.r.e 4
440.2.r.f 4
440.2.r.g 48
440.2.r.h 56
440.2.t $$\chi_{440}(197, \cdot)$$ 440.2.t.a 4 2
440.2.t.b 4
440.2.t.c 128
440.2.v $$\chi_{440}(153, \cdot)$$ 440.2.v.a 4 2
440.2.v.b 32
440.2.x $$\chi_{440}(23, \cdot)$$ None 0 2
440.2.y $$\chi_{440}(81, \cdot)$$ 440.2.y.a 8 4
440.2.y.b 12
440.2.y.c 12
440.2.y.d 16
440.2.z $$\chi_{440}(51, \cdot)$$ 440.2.z.a 192 4
440.2.bc $$\chi_{440}(39, \cdot)$$ None 0 4
440.2.bd $$\chi_{440}(69, \cdot)$$ 440.2.bd.a 272 4
440.2.bi $$\chi_{440}(141, \cdot)$$ 440.2.bi.a 8 4
440.2.bi.b 8
440.2.bi.c 176
440.2.bj $$\chi_{440}(151, \cdot)$$ None 0 4
440.2.bm $$\chi_{440}(19, \cdot)$$ 440.2.bm.a 8 4
440.2.bm.b 8
440.2.bm.c 256
440.2.bn $$\chi_{440}(9, \cdot)$$ 440.2.bn.a 72 4
440.2.bo $$\chi_{440}(17, \cdot)$$ 440.2.bo.a 144 8
440.2.bq $$\chi_{440}(47, \cdot)$$ None 0 8
440.2.bs $$\chi_{440}(3, \cdot)$$ 440.2.bs.a 544 8
440.2.bu $$\chi_{440}(13, \cdot)$$ 440.2.bu.a 544 8

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(440))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(440)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(110))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(220))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(440))$$$$^{\oplus 1}$$