# Properties

 Label 224.3 Level 224 Weight 3 Dimension 1606 Nonzero newspaces 12 Newform subspaces 26 Sturm bound 9216 Trace bound 13

## Defining parameters

 Level: $$N$$ = $$224 = 2^{5} \cdot 7$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$12$$ Newform subspaces: $$26$$ Sturm bound: $$9216$$ Trace bound: $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(224))$$.

Total New Old
Modular forms 3264 1706 1558
Cusp forms 2880 1606 1274
Eisenstein series 384 100 284

## Trace form

 $$1606 q - 16 q^{2} - 14 q^{3} - 16 q^{4} - 24 q^{5} - 16 q^{6} - 14 q^{7} - 40 q^{8} + 10 q^{9} + O(q^{10})$$ $$1606 q - 16 q^{2} - 14 q^{3} - 16 q^{4} - 24 q^{5} - 16 q^{6} - 14 q^{7} - 40 q^{8} + 10 q^{9} + 64 q^{10} + 18 q^{11} + 80 q^{12} + 40 q^{13} - 4 q^{14} - 20 q^{15} - 56 q^{16} - 88 q^{17} - 136 q^{18} - 78 q^{19} - 176 q^{20} - 84 q^{21} - 336 q^{22} + 118 q^{23} - 440 q^{24} + 6 q^{25} - 216 q^{26} + 244 q^{27} - 80 q^{28} + 16 q^{29} - 64 q^{30} - 18 q^{31} + 24 q^{32} - 52 q^{33} + 72 q^{34} - 110 q^{35} + 624 q^{36} + 104 q^{37} + 768 q^{38} - 340 q^{39} + 792 q^{40} + 120 q^{41} + 400 q^{42} - 48 q^{43} + 352 q^{44} + 592 q^{45} + 48 q^{46} + 286 q^{47} - 120 q^{48} + 110 q^{49} - 664 q^{50} - 234 q^{51} - 864 q^{52} + 136 q^{53} - 1208 q^{54} - 528 q^{55} - 576 q^{56} - 584 q^{57} - 1080 q^{58} - 622 q^{59} - 904 q^{60} - 504 q^{61} - 456 q^{62} - 498 q^{63} + 416 q^{64} - 412 q^{65} + 1136 q^{66} + 2 q^{67} + 712 q^{68} - 432 q^{69} + 640 q^{70} + 292 q^{71} + 1472 q^{72} - 8 q^{73} + 1040 q^{74} + 708 q^{75} + 1008 q^{76} - 180 q^{77} + 424 q^{78} + 1022 q^{79} - 648 q^{80} + 282 q^{81} - 1296 q^{82} + 1272 q^{83} - 1016 q^{84} - 384 q^{85} - 1400 q^{86} + 832 q^{87} - 1368 q^{88} - 200 q^{89} - 2632 q^{90} - 116 q^{91} - 1736 q^{92} - 1464 q^{93} - 2552 q^{94} - 594 q^{95} - 3368 q^{96} - 1144 q^{97} - 1880 q^{98} - 1328 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(224))$$

We only show spaces with odd 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
224.3.c $$\chi_{224}(97, \cdot)$$ 224.3.c.a 8 1
224.3.c.b 8
224.3.d $$\chi_{224}(127, \cdot)$$ 224.3.d.a 4 1
224.3.d.b 8
224.3.g $$\chi_{224}(15, \cdot)$$ 224.3.g.a 4 1
224.3.g.b 8
224.3.h $$\chi_{224}(209, \cdot)$$ 224.3.h.a 2 1
224.3.h.b 2
224.3.h.c 2
224.3.h.d 8
224.3.k $$\chi_{224}(71, \cdot)$$ None 0 2
224.3.l $$\chi_{224}(41, \cdot)$$ None 0 2
224.3.n $$\chi_{224}(17, \cdot)$$ 224.3.n.a 28 2
224.3.o $$\chi_{224}(79, \cdot)$$ 224.3.o.a 2 2
224.3.o.b 2
224.3.o.c 12
224.3.o.d 12
224.3.r $$\chi_{224}(95, \cdot)$$ 224.3.r.a 4 2
224.3.r.b 4
224.3.r.c 12
224.3.r.d 12
224.3.s $$\chi_{224}(33, \cdot)$$ 224.3.s.a 16 2
224.3.s.b 16
224.3.v $$\chi_{224}(13, \cdot)$$ 224.3.v.a 8 4
224.3.v.b 240
224.3.w $$\chi_{224}(43, \cdot)$$ 224.3.w.a 192 4
224.3.y $$\chi_{224}(23, \cdot)$$ None 0 4
224.3.bb $$\chi_{224}(73, \cdot)$$ None 0 4
224.3.bc $$\chi_{224}(5, \cdot)$$ 224.3.bc.a 496 8
224.3.bf $$\chi_{224}(11, \cdot)$$ 224.3.bf.a 496 8

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(224))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(224)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 2}$$