## Defining parameters

 Level: $$N$$ = $$29$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$2$$ Newform subspaces: $$2$$ Sturm bound: $$210$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(29))$$.

Total New Old
Modular forms 84 84 0
Cusp forms 56 56 0
Eisenstein series 28 28 0

## Trace form

 $$56q - 14q^{2} - 14q^{3} - 14q^{4} - 14q^{5} - 14q^{6} - 14q^{7} - 14q^{8} - 14q^{9} + O(q^{10})$$ $$56q - 14q^{2} - 14q^{3} - 14q^{4} - 14q^{5} - 14q^{6} - 14q^{7} - 14q^{8} - 14q^{9} - 14q^{10} - 14q^{11} - 14q^{12} - 14q^{13} - 14q^{14} - 14q^{15} - 14q^{16} - 14q^{17} - 14q^{18} - 14q^{19} + 154q^{20} + 182q^{21} + 154q^{22} + 56q^{23} + 322q^{24} + 70q^{25} + 56q^{26} + 28q^{27} - 42q^{29} - 196q^{30} - 98q^{31} - 238q^{32} - 224q^{33} - 224q^{34} - 210q^{35} - 686q^{36} - 140q^{37} - 294q^{38} - 322q^{39} - 266q^{40} - 14q^{41} - 14q^{42} - 14q^{43} + 168q^{44} + 406q^{45} + 756q^{46} + 266q^{47} + 994q^{48} + 434q^{49} + 672q^{50} + 322q^{51} + 546q^{52} + 238q^{53} + 364q^{54} + 210q^{55} + 140q^{56} - 182q^{58} - 84q^{59} - 574q^{60} - 238q^{61} - 504q^{62} - 686q^{63} - 896q^{64} - 518q^{65} - 1022q^{66} - 574q^{67} - 1092q^{68} - 686q^{69} - 1022q^{70} + 224q^{71} + 112q^{72} - 210q^{73} + 756q^{74} + 756q^{75} + 1106q^{76} + 616q^{77} + 882q^{78} + 182q^{79} + 1162q^{80} + 546q^{81} + 210q^{82} + 154q^{83} + 448q^{84} + 70q^{85} - 84q^{87} - 364q^{88} - 224q^{89} - 700q^{90} - 434q^{91} - 1022q^{92} - 406q^{93} - 462q^{94} - 1022q^{95} - 1176q^{96} + 560q^{97} - 168q^{98} + 868q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(29))$$

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
29.3.c $$\chi_{29}(12, \cdot)$$ 29.3.c.a 8 2
29.3.f $$\chi_{29}(2, \cdot)$$ 29.3.f.a 48 12