# Properties

 Label 28.3 Level 28 Weight 3 Dimension 22 Nonzero newspaces 4 Newforms 4 Sturm bound 144 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$28 = 2^{2} \cdot 7$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$4$$ Newforms: $$4$$ Sturm bound: $$144$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(28))$$.

Total New Old
Modular forms 63 30 33
Cusp forms 33 22 11
Eisenstein series 30 8 22

## Trace form

 $$22q - 3q^{2} + 3q^{3} - 3q^{4} - 3q^{5} - 6q^{6} - 4q^{7} - 21q^{8} - 42q^{9} + O(q^{10})$$ $$22q - 3q^{2} + 3q^{3} - 3q^{4} - 3q^{5} - 6q^{6} - 4q^{7} - 21q^{8} - 42q^{9} - 30q^{10} - 27q^{11} - 18q^{12} - 12q^{13} + 9q^{14} + 54q^{15} + 33q^{16} + 45q^{17} + 99q^{18} + 27q^{19} + 120q^{20} - 51q^{21} + 96q^{22} - 51q^{23} + 78q^{24} - 50q^{25} - 27q^{28} + 12q^{29} - 138q^{30} - 21q^{31} - 213q^{32} + 21q^{33} - 258q^{34} - 69q^{35} - 291q^{36} + 103q^{37} - 192q^{38} - 24q^{39} - 108q^{40} - 12q^{41} + 138q^{42} + 40q^{43} + 228q^{44} + 150q^{45} + 282q^{46} + 75q^{47} + 414q^{48} + 166q^{49} + 369q^{50} + 243q^{51} + 228q^{52} + 255q^{53} + 138q^{54} - 33q^{56} - 246q^{57} - 342q^{58} - 141q^{59} - 408q^{60} - 219q^{61} - 384q^{62} - 108q^{63} - 375q^{64} - 252q^{65} - 306q^{66} - 91q^{67} - 6q^{68} - 348q^{69} + 174q^{70} - 168q^{71} + 303q^{72} - 411q^{73} + 540q^{74} - 66q^{75} + 498q^{76} - 105q^{77} + 312q^{78} + 221q^{79} + 312q^{80} - 63q^{81} + 186q^{82} - 126q^{84} - 54q^{85} - 180q^{86} - 18q^{87} - 288q^{88} + 453q^{89} - 588q^{90} + 48q^{91} - 552q^{92} + 429q^{93} - 174q^{94} + 267q^{95} - 150q^{96} + 996q^{97} - 183q^{98} + 360q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(28))$$

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
28.3.b $$\chi_{28}(13, \cdot)$$ 28.3.b.a 2 1
28.3.c $$\chi_{28}(15, \cdot)$$ 28.3.c.a 6 1
28.3.g $$\chi_{28}(11, \cdot)$$ 28.3.g.a 12 2
28.3.h $$\chi_{28}(5, \cdot)$$ 28.3.h.a 2 2

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(28))$$ into lower level spaces

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