# Properties

 Label 105.4 Level 105 Weight 4 Dimension 728 Nonzero newspaces 12 Newform subspaces 27 Sturm bound 3072 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$105 = 3 \cdot 5 \cdot 7$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$12$$ Newform subspaces: $$27$$ Sturm bound: $$3072$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(105))$$.

Total New Old
Modular forms 1248 784 464
Cusp forms 1056 728 328
Eisenstein series 192 56 136

## Trace form

 $$728 q - 8 q^{2} - 6 q^{3} + 36 q^{4} + 12 q^{5} + 48 q^{6} + 104 q^{7} - 36 q^{8} - 54 q^{9} + O(q^{10})$$ $$728 q - 8 q^{2} - 6 q^{3} + 36 q^{4} + 12 q^{5} + 48 q^{6} + 104 q^{7} - 36 q^{8} - 54 q^{9} + 120 q^{10} + 112 q^{11} - 36 q^{12} - 184 q^{13} + 360 q^{14} - 174 q^{15} - 404 q^{16} - 56 q^{17} - 144 q^{18} - 628 q^{19} - 172 q^{20} - 606 q^{21} + 128 q^{22} + 912 q^{23} + 1044 q^{24} + 1574 q^{25} + 1948 q^{26} - 408 q^{27} + 2268 q^{28} - 472 q^{29} - 1722 q^{30} - 868 q^{31} - 1828 q^{32} - 306 q^{33} - 1576 q^{34} - 2012 q^{35} - 2244 q^{36} - 2364 q^{37} - 4748 q^{38} - 2028 q^{39} - 1712 q^{40} + 728 q^{41} - 3360 q^{42} - 1432 q^{43} - 448 q^{44} + 321 q^{45} + 2456 q^{46} + 880 q^{47} + 6252 q^{48} + 3832 q^{49} + 3700 q^{50} + 7002 q^{51} + 10584 q^{52} + 3976 q^{53} + 8736 q^{54} + 7812 q^{55} + 9468 q^{56} + 2460 q^{57} + 4904 q^{58} + 3616 q^{59} - 1704 q^{60} - 8124 q^{61} - 7056 q^{62} - 6618 q^{63} - 22284 q^{64} - 8936 q^{65} - 12588 q^{66} - 14204 q^{67} - 14920 q^{68} - 3600 q^{69} - 19800 q^{70} - 4072 q^{71} + 7896 q^{72} + 3644 q^{73} - 724 q^{74} + 6645 q^{75} + 11104 q^{76} + 216 q^{77} + 1320 q^{78} + 8068 q^{79} + 3752 q^{80} - 9546 q^{81} - 1944 q^{82} - 288 q^{83} - 7476 q^{84} + 3516 q^{85} + 388 q^{86} - 3396 q^{87} + 11520 q^{88} + 5256 q^{89} - 9876 q^{90} - 3248 q^{91} + 7296 q^{92} - 4986 q^{93} - 7864 q^{94} - 7952 q^{95} + 4896 q^{96} - 5592 q^{97} + 12932 q^{98} + 13956 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(105))$$

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
105.4.a $$\chi_{105}(1, \cdot)$$ 105.4.a.a 1 1
105.4.a.b 1
105.4.a.c 2
105.4.a.d 2
105.4.a.e 2
105.4.a.f 2
105.4.a.g 2
105.4.b $$\chi_{105}(41, \cdot)$$ 105.4.b.a 16 1
105.4.b.b 16
105.4.d $$\chi_{105}(64, \cdot)$$ 105.4.d.a 6 1
105.4.d.b 10
105.4.g $$\chi_{105}(104, \cdot)$$ 105.4.g.a 4 1
105.4.g.b 40
105.4.i $$\chi_{105}(16, \cdot)$$ 105.4.i.a 2 2
105.4.i.b 4
105.4.i.c 6
105.4.i.d 10
105.4.i.e 10
105.4.j $$\chi_{105}(8, \cdot)$$ 105.4.j.a 72 2
105.4.m $$\chi_{105}(13, \cdot)$$ 105.4.m.a 48 2
105.4.p $$\chi_{105}(59, \cdot)$$ 105.4.p.a 88 2
105.4.q $$\chi_{105}(4, \cdot)$$ 105.4.q.a 4 2
105.4.q.b 44
105.4.s $$\chi_{105}(26, \cdot)$$ 105.4.s.a 32 2
105.4.s.b 32
105.4.u $$\chi_{105}(52, \cdot)$$ 105.4.u.a 96 4
105.4.x $$\chi_{105}(2, \cdot)$$ 105.4.x.a 176 4

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(105))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(105)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 1}$$