# Properties

 Label 334.2.c Level $334$ Weight $2$ Character orbit 334.c Rep. character $\chi_{334}(3,\cdot)$ Character field $\Q(\zeta_{83})$ Dimension $1148$ Newform subspaces $2$ Sturm bound $84$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$334 = 2 \cdot 167$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 334.c (of order $$83$$ and degree $$82$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$167$$ Character field: $$\Q(\zeta_{83})$$ Newform subspaces: $$2$$ Sturm bound: $$84$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(334, [\chi])$$.

Total New Old
Modular forms 3608 1148 2460
Cusp forms 3280 1148 2132
Eisenstein series 328 0 328

## Trace form

 $$1148q - 14q^{4} - 2q^{5} - 4q^{6} - 26q^{9} + O(q^{10})$$ $$1148q - 14q^{4} - 2q^{5} - 4q^{6} - 26q^{9} - 2q^{10} - 16q^{11} - 14q^{13} - 12q^{14} - 28q^{15} - 14q^{16} - 28q^{17} - 8q^{18} - 16q^{19} - 2q^{20} - 48q^{21} - 4q^{22} - 28q^{23} - 4q^{24} - 30q^{25} - 18q^{26} - 36q^{27} - 28q^{29} - 20q^{30} - 20q^{31} - 56q^{33} - 12q^{34} - 80q^{35} - 26q^{36} - 26q^{37} - 16q^{38} - 60q^{39} - 2q^{40} - 68q^{41} - 36q^{42} - 38q^{43} - 16q^{44} - 74q^{45} - 32q^{46} - 40q^{47} - 42q^{49} - 32q^{50} - 68q^{51} - 14q^{52} - 66q^{53} - 28q^{54} - 60q^{55} - 12q^{56} - 76q^{57} - 78q^{59} - 28q^{60} - 52q^{61} - 40q^{62} - 64q^{63} - 14q^{64} - 56q^{65} - 32q^{66} - 54q^{67} - 28q^{68} - 80q^{69} - 40q^{70} - 68q^{71} - 8q^{72} - 36q^{73} - 30q^{74} - 80q^{75} - 16q^{76} - 120q^{77} - 52q^{78} - 80q^{79} - 2q^{80} - 102q^{81} - 28q^{82} - 94q^{83} - 48q^{84} - 116q^{85} - 34q^{86} - 148q^{87} - 4q^{88} - 112q^{89} - 78q^{90} - 96q^{91} - 28q^{92} - 88q^{93} - 68q^{94} - 152q^{95} - 4q^{96} - 88q^{97} - 32q^{98} - 184q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(334, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
334.2.c.a $$574$$ $$2.667$$ None $$-7$$ $$-2$$ $$-2$$ $$-6$$
334.2.c.b $$574$$ $$2.667$$ None $$7$$ $$2$$ $$0$$ $$6$$

## Decomposition of $$S_{2}^{\mathrm{old}}(334, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(334, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(167, [\chi])$$$$^{\oplus 2}$$