# Properties

 Label 229.2 Level 229 Weight 2 Dimension 2072 Nonzero newspaces 8 Newforms 12 Sturm bound 8740 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$229$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newforms: $$12$$ Sturm bound: $$8740$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(229))$$.

Total New Old
Modular forms 2299 2299 0
Cusp forms 2072 2072 0
Eisenstein series 227 227 0

## Trace form

 $$2072q$$ $$\mathstrut -\mathstrut 111q^{2}$$ $$\mathstrut -\mathstrut 110q^{3}$$ $$\mathstrut -\mathstrut 107q^{4}$$ $$\mathstrut -\mathstrut 108q^{5}$$ $$\mathstrut -\mathstrut 102q^{6}$$ $$\mathstrut -\mathstrut 106q^{7}$$ $$\mathstrut -\mathstrut 99q^{8}$$ $$\mathstrut -\mathstrut 101q^{9}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$2072q$$ $$\mathstrut -\mathstrut 111q^{2}$$ $$\mathstrut -\mathstrut 110q^{3}$$ $$\mathstrut -\mathstrut 107q^{4}$$ $$\mathstrut -\mathstrut 108q^{5}$$ $$\mathstrut -\mathstrut 102q^{6}$$ $$\mathstrut -\mathstrut 106q^{7}$$ $$\mathstrut -\mathstrut 99q^{8}$$ $$\mathstrut -\mathstrut 101q^{9}$$ $$\mathstrut -\mathstrut 96q^{10}$$ $$\mathstrut -\mathstrut 102q^{11}$$ $$\mathstrut -\mathstrut 86q^{12}$$ $$\mathstrut -\mathstrut 100q^{13}$$ $$\mathstrut -\mathstrut 90q^{14}$$ $$\mathstrut -\mathstrut 90q^{15}$$ $$\mathstrut -\mathstrut 83q^{16}$$ $$\mathstrut -\mathstrut 96q^{17}$$ $$\mathstrut -\mathstrut 75q^{18}$$ $$\mathstrut -\mathstrut 94q^{19}$$ $$\mathstrut -\mathstrut 72q^{20}$$ $$\mathstrut -\mathstrut 82q^{21}$$ $$\mathstrut -\mathstrut 78q^{22}$$ $$\mathstrut -\mathstrut 90q^{23}$$ $$\mathstrut -\mathstrut 54q^{24}$$ $$\mathstrut -\mathstrut 83q^{25}$$ $$\mathstrut -\mathstrut 72q^{26}$$ $$\mathstrut -\mathstrut 74q^{27}$$ $$\mathstrut -\mathstrut 58q^{28}$$ $$\mathstrut -\mathstrut 84q^{29}$$ $$\mathstrut -\mathstrut 42q^{30}$$ $$\mathstrut -\mathstrut 82q^{31}$$ $$\mathstrut -\mathstrut 51q^{32}$$ $$\mathstrut -\mathstrut 66q^{33}$$ $$\mathstrut -\mathstrut 60q^{34}$$ $$\mathstrut -\mathstrut 66q^{35}$$ $$\mathstrut -\mathstrut 23q^{36}$$ $$\mathstrut -\mathstrut 76q^{37}$$ $$\mathstrut -\mathstrut 54q^{38}$$ $$\mathstrut -\mathstrut 58q^{39}$$ $$\mathstrut -\mathstrut 24q^{40}$$ $$\mathstrut -\mathstrut 72q^{41}$$ $$\mathstrut -\mathstrut 18q^{42}$$ $$\mathstrut -\mathstrut 70q^{43}$$ $$\mathstrut -\mathstrut 30q^{44}$$ $$\mathstrut -\mathstrut 36q^{45}$$ $$\mathstrut -\mathstrut 42q^{46}$$ $$\mathstrut -\mathstrut 66q^{47}$$ $$\mathstrut +\mathstrut 10q^{48}$$ $$\mathstrut -\mathstrut 57q^{49}$$ $$\mathstrut -\mathstrut 21q^{50}$$ $$\mathstrut -\mathstrut 42q^{51}$$ $$\mathstrut -\mathstrut 16q^{52}$$ $$\mathstrut -\mathstrut 60q^{53}$$ $$\mathstrut +\mathstrut 6q^{54}$$ $$\mathstrut -\mathstrut 42q^{55}$$ $$\mathstrut +\mathstrut 6q^{56}$$ $$\mathstrut -\mathstrut 34q^{57}$$ $$\mathstrut -\mathstrut 24q^{58}$$ $$\mathstrut -\mathstrut 54q^{59}$$ $$\mathstrut +\mathstrut 54q^{60}$$ $$\mathstrut -\mathstrut 52q^{61}$$ $$\mathstrut -\mathstrut 18q^{62}$$ $$\mathstrut -\mathstrut 10q^{63}$$ $$\mathstrut +\mathstrut 13q^{64}$$ $$\mathstrut -\mathstrut 30q^{65}$$ $$\mathstrut +\mathstrut 30q^{66}$$ $$\mathstrut -\mathstrut 46q^{67}$$ $$\mathstrut +\mathstrut 12q^{68}$$ $$\mathstrut -\mathstrut 18q^{69}$$ $$\mathstrut +\mathstrut 30q^{70}$$ $$\mathstrut -\mathstrut 42q^{71}$$ $$\mathstrut +\mathstrut 81q^{72}$$ $$\mathstrut -\mathstrut 40q^{73}$$ $$\mathstrut +\mathstrut 10q^{75}$$ $$\mathstrut +\mathstrut 26q^{76}$$ $$\mathstrut -\mathstrut 18q^{77}$$ $$\mathstrut +\mathstrut 54q^{78}$$ $$\mathstrut -\mathstrut 34q^{79}$$ $$\mathstrut +\mathstrut 72q^{80}$$ $$\mathstrut +\mathstrut 7q^{81}$$ $$\mathstrut +\mathstrut 12q^{82}$$ $$\mathstrut -\mathstrut 30q^{83}$$ $$\mathstrut +\mathstrut 110q^{84}$$ $$\mathstrut -\mathstrut 6q^{85}$$ $$\mathstrut +\mathstrut 18q^{86}$$ $$\mathstrut +\mathstrut 6q^{87}$$ $$\mathstrut +\mathstrut 66q^{88}$$ $$\mathstrut -\mathstrut 24q^{89}$$ $$\mathstrut +\mathstrut 120q^{90}$$ $$\mathstrut -\mathstrut 2q^{91}$$ $$\mathstrut +\mathstrut 54q^{92}$$ $$\mathstrut +\mathstrut 14q^{93}$$ $$\mathstrut +\mathstrut 30q^{94}$$ $$\mathstrut +\mathstrut 6q^{95}$$ $$\mathstrut +\mathstrut 138q^{96}$$ $$\mathstrut -\mathstrut 16q^{97}$$ $$\mathstrut +\mathstrut 57q^{98}$$ $$\mathstrut +\mathstrut 42q^{99}$$ $$\mathstrut +\mathstrut O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(229))$$

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
229.2.a $$\chi_{229}(1, \cdot)$$ 229.2.a.a 1 1
229.2.a.b 6
229.2.a.c 11
229.2.b $$\chi_{229}(228, \cdot)$$ 229.2.b.a 2 1
229.2.b.b 16
229.2.c $$\chi_{229}(94, \cdot)$$ 229.2.c.a 36 2
229.2.e $$\chi_{229}(95, \cdot)$$ 229.2.e.a 2 2
229.2.e.b 36
229.2.g $$\chi_{229}(16, \cdot)$$ 229.2.g.a 306 18
229.2.h $$\chi_{229}(4, \cdot)$$ 229.2.h.a 324 18
229.2.i $$\chi_{229}(3, \cdot)$$ 229.2.i.a 648 36
229.2.k $$\chi_{229}(5, \cdot)$$ 229.2.k.a 684 36