# Properties

 Label 201.2.m Level 201 Weight 2 Character orbit m Rep. character $$\chi_{201}(4,\cdot)$$ Character field $$\Q(\zeta_{33})$$ Dimension 220 Newforms 2 Sturm bound 45 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$201 = 3 \cdot 67$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 201.m (of order $$33$$ and degree $$20$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$67$$ Character field: $$\Q(\zeta_{33})$$ Newforms: $$2$$ Sturm bound: $$45$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(201, [\chi])$$.

Total New Old
Modular forms 500 220 280
Cusp forms 420 220 200
Eisenstein series 80 0 80

## Trace form

 $$220q + 4q^{2} - 2q^{3} + 14q^{4} + 6q^{7} - 78q^{8} - 22q^{9} + O(q^{10})$$ $$220q + 4q^{2} - 2q^{3} + 14q^{4} + 6q^{7} - 78q^{8} - 22q^{9} - 54q^{10} - 6q^{11} + 2q^{12} + 3q^{13} + 12q^{14} - 18q^{15} + 20q^{16} - 4q^{17} + 4q^{18} - 16q^{19} - 16q^{20} + 4q^{21} - 58q^{22} + 2q^{23} + 12q^{24} - 14q^{25} + 20q^{26} - 2q^{27} - 8q^{28} - 24q^{29} - 48q^{30} - 15q^{31} - 104q^{32} - 2q^{33} + 32q^{34} - 30q^{35} - 8q^{36} - 30q^{37} - 6q^{38} + 9q^{39} - 122q^{40} - 72q^{41} - 32q^{42} - 52q^{43} - 32q^{44} - 38q^{46} + 20q^{48} + 17q^{49} - 40q^{50} - 118q^{52} + 84q^{53} - 22q^{55} + 232q^{56} - 21q^{57} + 48q^{58} + 32q^{59} + 192q^{60} + 29q^{61} + 20q^{62} - 5q^{63} - 18q^{64} + 176q^{65} + 152q^{66} + 35q^{67} - 216q^{68} + 44q^{69} + 64q^{70} + 148q^{71} + 76q^{72} - 96q^{73} + 34q^{74} + 74q^{75} + 164q^{76} - 80q^{77} + 122q^{78} - 60q^{79} + 294q^{80} - 22q^{81} - 144q^{82} + 30q^{83} - 158q^{84} - 6q^{85} - 194q^{86} + 22q^{87} - 140q^{88} - 58q^{89} - 54q^{90} - 52q^{91} - 36q^{92} + 5q^{93} - 136q^{94} - 56q^{95} - 12q^{96} - 81q^{97} - 86q^{98} - 6q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(201, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
201.2.m.a $$100$$ $$1.605$$ None $$2$$ $$10$$ $$-2$$ $$1$$
201.2.m.b $$120$$ $$1.605$$ None $$2$$ $$-12$$ $$2$$ $$5$$

## Decomposition of $$S_{2}^{\mathrm{old}}(201, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(201, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(67, [\chi])$$$$^{\oplus 2}$$