# Properties

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

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## 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

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

## 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

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