# Properties

 Label 473.2.bb Level 473 Weight 2 Character orbit bb Rep. character $$\chi_{473}(2,\cdot)$$ Character field $$\Q(\zeta_{70})$$ Dimension 1008 Newforms 1 Sturm bound 88 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$473 = 11 \cdot 43$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 473.bb (of order $$70$$ and degree $$24$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$473$$ Character field: $$\Q(\zeta_{70})$$ Newforms: $$1$$ Sturm bound: $$88$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(473, [\chi])$$.

Total New Old
Modular forms 1104 1104 0
Cusp forms 1008 1008 0
Eisenstein series 96 96 0

## Trace form

 $$1008q - 35q^{2} - 21q^{3} + 21q^{4} - 21q^{5} - 50q^{6} - 105q^{8} - 65q^{9} + O(q^{10})$$ $$1008q - 35q^{2} - 21q^{3} + 21q^{4} - 21q^{5} - 50q^{6} - 105q^{8} - 65q^{9} - 24q^{11} - 84q^{12} - 20q^{13} + 19q^{14} + 17q^{15} - 39q^{16} - 35q^{17} - 35q^{18} + 70q^{19} + 7q^{20} - 49q^{22} - 58q^{23} + 30q^{24} - 65q^{25} - 7q^{26} - 21q^{27} - 35q^{28} - 35q^{29} - 35q^{30} - 13q^{31} - 126q^{33} - 14q^{34} + 65q^{35} + 176q^{36} - 77q^{38} - 35q^{39} + 5q^{40} - 25q^{41} + 332q^{44} + 98q^{45} - 35q^{46} - 51q^{47} + 63q^{48} - 178q^{49} - 35q^{51} + 95q^{52} - 75q^{53} - 98q^{55} - 62q^{56} - 55q^{57} - 95q^{58} - 113q^{59} + 39q^{60} - 35q^{62} - 35q^{63} + 17q^{64} - 206q^{66} - 150q^{67} - 470q^{68} + 147q^{69} - 140q^{70} - 7q^{71} - 245q^{72} - 35q^{73} - 135q^{74} + 56q^{75} + 70q^{77} - 258q^{78} + 202q^{81} + 105q^{82} - 50q^{83} - 10q^{84} + 187q^{86} + 161q^{88} - 42q^{89} - 295q^{90} + 77q^{91} + 108q^{92} + 385q^{94} - 195q^{95} - 105q^{96} + 152q^{97} - 83q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(473, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
473.2.bb.a $$1008$$ $$3.777$$ None $$-35$$ $$-21$$ $$-21$$ $$0$$