# Properties

 Label 28.4 Level 28 Weight 4 Dimension 36 Nonzero newspaces 4 Newform subspaces 6 Sturm bound 192 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$28 = 2^{2} \cdot 7$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$4$$ Newform subspaces: $$6$$ Sturm bound: $$192$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(28))$$.

Total New Old
Modular forms 87 48 39
Cusp forms 57 36 21
Eisenstein series 30 12 18

## Trace form

 $$36 q - 3 q^{2} - 6 q^{3} - 3 q^{4} + 6 q^{5} + 24 q^{7} + 45 q^{8} + 36 q^{9} + O(q^{10})$$ $$36 q - 3 q^{2} - 6 q^{3} - 3 q^{4} + 6 q^{5} + 24 q^{7} + 45 q^{8} + 36 q^{9} - 12 q^{10} - 84 q^{11} - 168 q^{12} - 150 q^{13} - 159 q^{14} - 192 q^{15} - 87 q^{16} + 60 q^{17} + 21 q^{18} + 318 q^{19} + 642 q^{21} + 126 q^{22} + 84 q^{23} + 348 q^{24} - 552 q^{25} + 396 q^{26} - 612 q^{27} + 645 q^{28} - 900 q^{29} + 900 q^{30} + 336 q^{31} + 837 q^{32} + 900 q^{33} + 498 q^{35} - 1011 q^{36} + 540 q^{37} - 1620 q^{38} - 504 q^{39} - 1548 q^{40} - 1080 q^{41} - 2004 q^{42} - 444 q^{43} - 2082 q^{44} - 1014 q^{45} - 1158 q^{46} - 288 q^{47} + 348 q^{49} + 1449 q^{50} + 756 q^{51} + 2592 q^{52} + 1128 q^{53} + 4572 q^{54} + 1872 q^{55} + 3537 q^{56} + 1716 q^{57} + 2514 q^{58} + 870 q^{59} + 2208 q^{60} - 270 q^{61} - 948 q^{63} - 1767 q^{64} + 324 q^{65} - 4272 q^{66} - 672 q^{67} - 6084 q^{68} + 468 q^{69} - 7344 q^{70} + 504 q^{71} - 5991 q^{72} - 708 q^{73} - 1914 q^{74} - 1818 q^{75} - 3192 q^{77} + 3624 q^{78} - 1092 q^{79} + 7032 q^{80} - 672 q^{81} + 7692 q^{82} + 1830 q^{83} + 10668 q^{84} + 1668 q^{85} + 7350 q^{86} - 468 q^{87} + 3570 q^{88} - 5268 q^{89} - 2010 q^{91} - 3366 q^{92} - 6096 q^{93} - 6780 q^{94} - 924 q^{95} - 11784 q^{96} + 960 q^{97} - 9759 q^{98} - 2148 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(28))$$

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
28.4.a $$\chi_{28}(1, \cdot)$$ 28.4.a.a 1 1
28.4.a.b 1
28.4.d $$\chi_{28}(27, \cdot)$$ 28.4.d.a 2 1
28.4.d.b 8
28.4.e $$\chi_{28}(9, \cdot)$$ 28.4.e.a 4 2
28.4.f $$\chi_{28}(3, \cdot)$$ 28.4.f.a 20 2

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(28))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(28)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 2}$$