## Defining parameters

 Level: $$N$$ = $$29$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$4$$ Newforms: $$4$$ Sturm bound: $$140$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(29))$$.

Total New Old
Modular forms 49 49 0
Cusp forms 22 22 0
Eisenstein series 27 27 0

## Trace form

 $$22q - 11q^{2} - 10q^{3} - 7q^{4} - 8q^{5} - 2q^{6} - 6q^{7} + q^{8} - q^{9} + O(q^{10})$$ $$22q - 11q^{2} - 10q^{3} - 7q^{4} - 8q^{5} - 2q^{6} - 6q^{7} + q^{8} - q^{9} + 4q^{10} - 2q^{11} + 14q^{12} + 10q^{14} + 10q^{15} + 17q^{16} + 4q^{17} + 25q^{18} + 6q^{19} + 7q^{20} - 10q^{21} - 6q^{22} - 4q^{23} - 38q^{24} - 11q^{25} - 7q^{26} - 16q^{27} - 28q^{28} - 13q^{29} - 40q^{30} - 10q^{31} - 7q^{32} - 8q^{33} + 5q^{34} + 6q^{35} - 7q^{36} + 10q^{37} + 18q^{38} + 14q^{39} + 55q^{40} + 28q^{41} + 82q^{42} + 30q^{43} + 56q^{44} + 29q^{45} - 12q^{46} + 6q^{47} - 2q^{48} - 13q^{49} - 19q^{50} + 2q^{51} - 28q^{52} - 23q^{53} - 20q^{54} - 54q^{55} - 20q^{56} - 4q^{57} - 95q^{58} + 4q^{59} - 42q^{60} - 8q^{61} - 16q^{62} - 22q^{63} - 13q^{64} + 7q^{65} + 18q^{66} - 2q^{67} + 14q^{68} + 26q^{69} - 10q^{70} - 12q^{71} + 27q^{72} - 3q^{73} + 2q^{74} + 40q^{75} + 14q^{76} + 12q^{77} + 42q^{78} + 38q^{79} - 24q^{80} - 5q^{81} + 56q^{82} + 14q^{83} + 10q^{85} - 36q^{86} + 32q^{87} - 16q^{88} + 6q^{89} + 38q^{90} + 14q^{91} - 14q^{92} + 58q^{93} + 74q^{94} - 6q^{95} + 7q^{97} - 25q^{98} - 40q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$

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
29.2.a $$\chi_{29}(1, \cdot)$$ 29.2.a.a 2 1
29.2.b $$\chi_{29}(28, \cdot)$$ 29.2.b.a 2 1
29.2.d $$\chi_{29}(7, \cdot)$$ 29.2.d.a 6 6
29.2.e $$\chi_{29}(4, \cdot)$$ 29.2.e.a 12 6