# Properties

 Label 224.6 Level 224 Weight 6 Dimension 4090 Nonzero newspaces 12 Sturm bound 18432 Trace bound 13

## Defining parameters

 Level: $$N$$ = $$224 = 2^{5} \cdot 7$$ Weight: $$k$$ = $$6$$ Nonzero newspaces: $$12$$ Sturm bound: $$18432$$ Trace bound: $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_1(224))$$.

Total New Old
Modular forms 7872 4190 3682
Cusp forms 7488 4090 3398
Eisenstein series 384 100 284

## Trace form

 $$4090 q - 16 q^{2} - 10 q^{3} - 16 q^{4} - 92 q^{5} - 16 q^{6} + 82 q^{7} - 40 q^{8} - 598 q^{9} + O(q^{10})$$ $$4090 q - 16 q^{2} - 10 q^{3} - 16 q^{4} - 92 q^{5} - 16 q^{6} + 82 q^{7} - 40 q^{8} - 598 q^{9} + 384 q^{10} - 10 q^{11} + 3152 q^{12} - 236 q^{13} - 2500 q^{14} - 868 q^{15} - 8376 q^{16} - 3632 q^{17} + 3224 q^{18} - 10 q^{19} + 15184 q^{20} + 5868 q^{21} + 24720 q^{22} + 1318 q^{23} - 42936 q^{24} + 5414 q^{25} - 25976 q^{26} + 14912 q^{27} + 2160 q^{28} - 7396 q^{29} + 64608 q^{30} - 71986 q^{31} + 37144 q^{32} - 21708 q^{33} + 12488 q^{34} + 4762 q^{35} - 131216 q^{36} + 14500 q^{37} - 832 q^{38} + 158548 q^{39} + 57880 q^{40} + 70640 q^{41} + 53600 q^{42} - 112280 q^{43} - 7456 q^{44} - 57588 q^{45} - 126672 q^{46} - 11574 q^{47} - 224760 q^{48} + 160194 q^{49} + 9000 q^{50} + 15266 q^{51} - 36960 q^{52} + 146804 q^{53} - 2648 q^{54} - 194356 q^{55} + 80960 q^{56} + 22208 q^{57} + 169128 q^{58} + 14470 q^{59} + 92152 q^{60} - 333948 q^{61} - 126984 q^{62} + 247170 q^{63} + 98336 q^{64} + 65244 q^{65} + 290000 q^{66} + 256194 q^{67} + 302408 q^{68} + 417344 q^{69} + 56272 q^{70} - 66920 q^{71} - 54208 q^{72} + 160656 q^{73} - 426224 q^{74} - 430256 q^{75} - 512016 q^{76} - 180452 q^{77} - 167064 q^{78} - 495762 q^{79} + 194168 q^{80} - 596522 q^{81} - 870416 q^{82} + 658464 q^{83} - 597496 q^{84} + 237208 q^{85} - 539800 q^{86} + 1178644 q^{87} + 399656 q^{88} + 518640 q^{89} + 1600280 q^{90} - 99284 q^{91} + 2240184 q^{92} + 811768 q^{93} + 2086856 q^{94} - 1617054 q^{95} - 187432 q^{96} - 1404432 q^{97} - 1539928 q^{98} - 1410984 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_1(224))$$

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
224.6.a $$\chi_{224}(1, \cdot)$$ 224.6.a.a 1 1
224.6.a.b 1
224.6.a.c 2
224.6.a.d 2
224.6.a.e 3
224.6.a.f 3
224.6.a.g 4
224.6.a.h 4
224.6.a.i 5
224.6.a.j 5
224.6.b $$\chi_{224}(113, \cdot)$$ 224.6.b.a 14 1
224.6.b.b 16
224.6.e $$\chi_{224}(111, \cdot)$$ 224.6.e.a 2 1
224.6.e.b 36
224.6.f $$\chi_{224}(223, \cdot)$$ 224.6.f.a 40 1
224.6.i $$\chi_{224}(65, \cdot)$$ 224.6.i.a 20 2
224.6.i.b 20
224.6.i.c 20
224.6.i.d 20
224.6.j $$\chi_{224}(55, \cdot)$$ None 0 2
224.6.m $$\chi_{224}(57, \cdot)$$ None 0 2
224.6.p $$\chi_{224}(31, \cdot)$$ 224.6.p.a 80 2
224.6.q $$\chi_{224}(47, \cdot)$$ 224.6.q.a 76 2
224.6.t $$\chi_{224}(81, \cdot)$$ 224.6.t.a 76 2
224.6.u $$\chi_{224}(29, \cdot)$$ n/a 480 4
224.6.x $$\chi_{224}(27, \cdot)$$ n/a 632 4
224.6.z $$\chi_{224}(87, \cdot)$$ None 0 4
224.6.ba $$\chi_{224}(9, \cdot)$$ None 0 4
224.6.bd $$\chi_{224}(37, \cdot)$$ n/a 1264 8
224.6.be $$\chi_{224}(3, \cdot)$$ n/a 1264 8

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_1(224))$$ into lower level spaces

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