# Properties

 Label 334.2 Level 334 Weight 2 Dimension 1161 Nonzero newspaces 2 Newforms 8 Sturm bound 13944 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$334 = 2 \cdot 167$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$2$$ Newforms: $$8$$ Sturm bound: $$13944$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(334))$$.

Total New Old
Modular forms 3652 1161 2491
Cusp forms 3321 1161 2160
Eisenstein series 331 0 331

## Trace form

 $$1161q$$ $$\mathstrut -\mathstrut q^{2}$$ $$\mathstrut -\mathstrut 4q^{3}$$ $$\mathstrut -\mathstrut q^{4}$$ $$\mathstrut -\mathstrut 6q^{5}$$ $$\mathstrut -\mathstrut 4q^{6}$$ $$\mathstrut -\mathstrut 8q^{7}$$ $$\mathstrut -\mathstrut q^{8}$$ $$\mathstrut -\mathstrut 13q^{9}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$1161q$$ $$\mathstrut -\mathstrut q^{2}$$ $$\mathstrut -\mathstrut 4q^{3}$$ $$\mathstrut -\mathstrut q^{4}$$ $$\mathstrut -\mathstrut 6q^{5}$$ $$\mathstrut -\mathstrut 4q^{6}$$ $$\mathstrut -\mathstrut 8q^{7}$$ $$\mathstrut -\mathstrut q^{8}$$ $$\mathstrut -\mathstrut 13q^{9}$$ $$\mathstrut -\mathstrut 6q^{10}$$ $$\mathstrut -\mathstrut 12q^{11}$$ $$\mathstrut -\mathstrut 4q^{12}$$ $$\mathstrut -\mathstrut 14q^{13}$$ $$\mathstrut -\mathstrut 8q^{14}$$ $$\mathstrut -\mathstrut 24q^{15}$$ $$\mathstrut -\mathstrut q^{16}$$ $$\mathstrut -\mathstrut 18q^{17}$$ $$\mathstrut -\mathstrut 13q^{18}$$ $$\mathstrut -\mathstrut 20q^{19}$$ $$\mathstrut -\mathstrut 6q^{20}$$ $$\mathstrut -\mathstrut 32q^{21}$$ $$\mathstrut -\mathstrut 12q^{22}$$ $$\mathstrut -\mathstrut 24q^{23}$$ $$\mathstrut -\mathstrut 4q^{24}$$ $$\mathstrut -\mathstrut 31q^{25}$$ $$\mathstrut -\mathstrut 14q^{26}$$ $$\mathstrut -\mathstrut 40q^{27}$$ $$\mathstrut -\mathstrut 8q^{28}$$ $$\mathstrut -\mathstrut 30q^{29}$$ $$\mathstrut -\mathstrut 24q^{30}$$ $$\mathstrut -\mathstrut 32q^{31}$$ $$\mathstrut -\mathstrut q^{32}$$ $$\mathstrut -\mathstrut 48q^{33}$$ $$\mathstrut -\mathstrut 18q^{34}$$ $$\mathstrut -\mathstrut 48q^{35}$$ $$\mathstrut -\mathstrut 13q^{36}$$ $$\mathstrut -\mathstrut 38q^{37}$$ $$\mathstrut -\mathstrut 20q^{38}$$ $$\mathstrut -\mathstrut 56q^{39}$$ $$\mathstrut -\mathstrut 6q^{40}$$ $$\mathstrut -\mathstrut 42q^{41}$$ $$\mathstrut -\mathstrut 32q^{42}$$ $$\mathstrut -\mathstrut 44q^{43}$$ $$\mathstrut -\mathstrut 12q^{44}$$ $$\mathstrut -\mathstrut 78q^{45}$$ $$\mathstrut -\mathstrut 24q^{46}$$ $$\mathstrut -\mathstrut 48q^{47}$$ $$\mathstrut -\mathstrut 4q^{48}$$ $$\mathstrut -\mathstrut 57q^{49}$$ $$\mathstrut -\mathstrut 31q^{50}$$ $$\mathstrut -\mathstrut 72q^{51}$$ $$\mathstrut -\mathstrut 14q^{52}$$ $$\mathstrut -\mathstrut 54q^{53}$$ $$\mathstrut -\mathstrut 40q^{54}$$ $$\mathstrut -\mathstrut 72q^{55}$$ $$\mathstrut -\mathstrut 8q^{56}$$ $$\mathstrut -\mathstrut 80q^{57}$$ $$\mathstrut -\mathstrut 30q^{58}$$ $$\mathstrut -\mathstrut 60q^{59}$$ $$\mathstrut -\mathstrut 24q^{60}$$ $$\mathstrut -\mathstrut 62q^{61}$$ $$\mathstrut -\mathstrut 32q^{62}$$ $$\mathstrut -\mathstrut 104q^{63}$$ $$\mathstrut -\mathstrut q^{64}$$ $$\mathstrut -\mathstrut 84q^{65}$$ $$\mathstrut -\mathstrut 48q^{66}$$ $$\mathstrut -\mathstrut 68q^{67}$$ $$\mathstrut -\mathstrut 18q^{68}$$ $$\mathstrut -\mathstrut 96q^{69}$$ $$\mathstrut -\mathstrut 48q^{70}$$ $$\mathstrut -\mathstrut 72q^{71}$$ $$\mathstrut -\mathstrut 13q^{72}$$ $$\mathstrut -\mathstrut 74q^{73}$$ $$\mathstrut -\mathstrut 38q^{74}$$ $$\mathstrut -\mathstrut 124q^{75}$$ $$\mathstrut -\mathstrut 20q^{76}$$ $$\mathstrut -\mathstrut 96q^{77}$$ $$\mathstrut -\mathstrut 56q^{78}$$ $$\mathstrut -\mathstrut 80q^{79}$$ $$\mathstrut -\mathstrut 6q^{80}$$ $$\mathstrut -\mathstrut 121q^{81}$$ $$\mathstrut -\mathstrut 42q^{82}$$ $$\mathstrut -\mathstrut 84q^{83}$$ $$\mathstrut -\mathstrut 32q^{84}$$ $$\mathstrut -\mathstrut 108q^{85}$$ $$\mathstrut -\mathstrut 44q^{86}$$ $$\mathstrut -\mathstrut 120q^{87}$$ $$\mathstrut -\mathstrut 12q^{88}$$ $$\mathstrut -\mathstrut 90q^{89}$$ $$\mathstrut -\mathstrut 78q^{90}$$ $$\mathstrut -\mathstrut 112q^{91}$$ $$\mathstrut -\mathstrut 24q^{92}$$ $$\mathstrut -\mathstrut 128q^{93}$$ $$\mathstrut -\mathstrut 48q^{94}$$ $$\mathstrut -\mathstrut 120q^{95}$$ $$\mathstrut -\mathstrut 4q^{96}$$ $$\mathstrut -\mathstrut 98q^{97}$$ $$\mathstrut -\mathstrut 57q^{98}$$ $$\mathstrut -\mathstrut 156q^{99}$$ $$\mathstrut +\mathstrut O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(334))$$

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
334.2.a $$\chi_{334}(1, \cdot)$$ 334.2.a.a 1 1
334.2.a.b 2
334.2.a.c 2
334.2.a.d 2
334.2.a.e 3
334.2.a.f 3
334.2.c $$\chi_{334}(3, \cdot)$$ 334.2.c.a 574 82
334.2.c.b 574

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(334))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(334)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(167))$$$$^{\oplus 2}$$