# Properties

 Label 501.2.e Level $501$ Weight $2$ Character orbit 501.e Rep. character $\chi_{501}(4,\cdot)$ Character field $\Q(\zeta_{83})$ Dimension $2296$ Newform subspaces $2$ Sturm bound $112$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$501 = 3 \cdot 167$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 501.e (of order $$83$$ and degree $$82$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$167$$ Character field: $$\Q(\zeta_{83})$$ Newform subspaces: $$2$$ Sturm bound: $$112$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(501, [\chi])$$.

Total New Old
Modular forms 4756 2296 2460
Cusp forms 4428 2296 2132
Eisenstein series 328 0 328

## Trace form

 $$2296q - 32q^{4} - 4q^{6} - 28q^{9} + O(q^{10})$$ $$2296q - 32q^{4} - 4q^{6} - 28q^{9} - 16q^{10} - 12q^{11} - 8q^{12} - 12q^{13} - 32q^{14} - 8q^{15} - 64q^{16} - 16q^{17} - 24q^{19} - 36q^{20} - 36q^{22} - 16q^{23} - 12q^{24} - 40q^{25} - 64q^{26} - 36q^{28} - 20q^{29} - 28q^{30} - 24q^{31} - 40q^{32} - 8q^{33} - 56q^{34} - 44q^{35} - 32q^{36} - 24q^{37} - 80q^{38} - 16q^{39} - 132q^{40} - 52q^{41} - 20q^{42} - 60q^{43} - 84q^{44} - 80q^{46} - 60q^{47} - 32q^{48} - 68q^{49} - 80q^{50} - 20q^{51} - 72q^{52} - 56q^{53} - 4q^{54} - 96q^{55} - 116q^{56} - 8q^{57} - 44q^{58} - 92q^{59} - 48q^{60} - 64q^{61} - 76q^{62} - 128q^{64} - 68q^{65} - 16q^{66} - 60q^{67} - 172q^{68} - 28q^{69} - 136q^{70} - 108q^{71} - 40q^{73} - 108q^{74} - 24q^{75} - 120q^{76} - 96q^{77} - 40q^{78} - 104q^{79} - 144q^{80} - 28q^{81} - 164q^{82} - 120q^{83} - 40q^{84} - 84q^{85} - 56q^{86} - 40q^{87} - 176q^{88} - 84q^{89} - 16q^{90} - 104q^{91} - 108q^{92} - 136q^{94} - 152q^{95} - 88q^{96} - 52q^{97} - 112q^{98} - 12q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(501, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
501.2.e.a $$1148$$ $$4.001$$ None $$-2$$ $$-14$$ $$-4$$ $$0$$
501.2.e.b $$1148$$ $$4.001$$ None $$2$$ $$14$$ $$4$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(501, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(501, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(167, [\chi])$$$$^{\oplus 2}$$