# Properties

 Label 224.2 Level 224 Weight 2 Dimension 778 Nonzero newspaces 12 Newform subspaces 23 Sturm bound 6144 Trace bound 13

## Defining parameters

 Level: $$N$$ = $$224 = 2^{5} \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Newform subspaces: $$23$$ Sturm bound: $$6144$$ Trace bound: $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(224))$$.

Total New Old
Modular forms 1728 878 850
Cusp forms 1345 778 567
Eisenstein series 383 100 283

## Trace form

 $$778 q - 16 q^{2} - 10 q^{3} - 16 q^{4} - 12 q^{5} - 16 q^{6} - 14 q^{7} - 40 q^{8} - 22 q^{9} + O(q^{10})$$ $$778 q - 16 q^{2} - 10 q^{3} - 16 q^{4} - 12 q^{5} - 16 q^{6} - 14 q^{7} - 40 q^{8} - 22 q^{9} - 32 q^{10} - 10 q^{11} - 48 q^{12} - 28 q^{13} - 36 q^{14} - 36 q^{15} - 56 q^{16} - 16 q^{17} - 56 q^{18} - 10 q^{19} - 48 q^{20} - 20 q^{21} - 64 q^{22} - 26 q^{23} + 8 q^{24} - 26 q^{25} + 24 q^{26} - 64 q^{27} - 20 q^{29} + 48 q^{30} - 50 q^{31} + 24 q^{32} - 44 q^{33} + 8 q^{34} - 38 q^{35} + 16 q^{36} - 12 q^{37} - 32 q^{38} - 76 q^{39} - 40 q^{40} - 48 q^{41} - 40 q^{42} - 56 q^{43} - 96 q^{44} - 100 q^{45} - 80 q^{46} - 54 q^{47} - 120 q^{48} - 46 q^{49} - 120 q^{50} - 62 q^{51} - 32 q^{52} - 124 q^{53} - 40 q^{54} + 12 q^{55} - 32 q^{56} - 160 q^{57} - 8 q^{58} + 6 q^{59} - 8 q^{60} - 108 q^{61} + 24 q^{62} - 30 q^{63} + 32 q^{64} - 68 q^{65} + 32 q^{66} + 34 q^{67} - 56 q^{68} - 128 q^{69} - 8 q^{70} + 24 q^{71} - 64 q^{72} - 16 q^{73} - 48 q^{74} - 16 q^{75} - 16 q^{76} - 36 q^{77} - 120 q^{78} - 18 q^{79} - 8 q^{80} + 6 q^{81} - 16 q^{82} - 96 q^{83} - 40 q^{84} - 72 q^{85} + 24 q^{86} - 140 q^{87} - 24 q^{88} - 48 q^{89} + 104 q^{90} - 20 q^{91} + 56 q^{92} + 56 q^{93} + 104 q^{94} - 94 q^{95} + 216 q^{96} + 16 q^{97} + 168 q^{98} - 72 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(224))$$

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
224.2.a $$\chi_{224}(1, \cdot)$$ 224.2.a.a 1 1
224.2.a.b 1
224.2.a.c 2
224.2.a.d 2
224.2.b $$\chi_{224}(113, \cdot)$$ 224.2.b.a 2 1
224.2.b.b 4
224.2.e $$\chi_{224}(111, \cdot)$$ 224.2.e.a 2 1
224.2.e.b 4
224.2.f $$\chi_{224}(223, \cdot)$$ 224.2.f.a 8 1
224.2.i $$\chi_{224}(65, \cdot)$$ 224.2.i.a 4 2
224.2.i.b 4
224.2.i.c 4
224.2.i.d 4
224.2.j $$\chi_{224}(55, \cdot)$$ None 0 2
224.2.m $$\chi_{224}(57, \cdot)$$ None 0 2
224.2.p $$\chi_{224}(31, \cdot)$$ 224.2.p.a 16 2
224.2.q $$\chi_{224}(47, \cdot)$$ 224.2.q.a 12 2
224.2.t $$\chi_{224}(81, \cdot)$$ 224.2.t.a 12 2
224.2.u $$\chi_{224}(29, \cdot)$$ 224.2.u.a 4 4
224.2.u.b 40
224.2.u.c 52
224.2.x $$\chi_{224}(27, \cdot)$$ 224.2.x.a 8 4
224.2.x.b 112
224.2.z $$\chi_{224}(87, \cdot)$$ None 0 4
224.2.ba $$\chi_{224}(9, \cdot)$$ None 0 4
224.2.bd $$\chi_{224}(37, \cdot)$$ 224.2.bd.a 240 8
224.2.be $$\chi_{224}(3, \cdot)$$ 224.2.be.a 240 8

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(224))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(224)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 2}$$