# Properties

 Label 473.2.v Level 473 Weight 2 Character orbit v Rep. character $$\chi_{473}(4,\cdot)$$ Character field $$\Q(\zeta_{35})$$ 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.v (of order $$35$$ and degree $$24$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$473$$ Character field: $$\Q(\zeta_{35})$$ 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

 $$1008q - 21q^{2} - 19q^{3} + 21q^{4} - 19q^{5} - 38q^{6} - 6q^{7} - 63q^{8} + 11q^{9} + O(q^{10})$$ $$1008q - 21q^{2} - 19q^{3} + 21q^{4} - 19q^{5} - 38q^{6} - 6q^{7} - 63q^{8} + 11q^{9} - 64q^{10} - 24q^{11} - 60q^{12} + 8q^{13} + 3q^{14} - 7q^{15} + 49q^{16} - 23q^{17} + 37q^{18} - 76q^{19} - 15q^{20} - 10q^{21} - 29q^{22} - 106q^{23} - 20q^{24} + 27q^{25} - 21q^{26} - 13q^{27} + 23q^{28} - 43q^{29} + 97q^{30} - 25q^{31} + 12q^{32} - 66q^{33} + 30q^{34} + 85q^{35} - 212q^{36} - 92q^{37} - 149q^{38} - 79q^{39} + 87q^{40} - 45q^{41} + 100q^{42} + 26q^{43} - 340q^{44} + 18q^{45} + 105q^{46} - 27q^{47} - 99q^{48} - 194q^{49} + 108q^{50} + 53q^{51} + 25q^{52} - 79q^{53} - 50q^{54} + 44q^{55} + 66q^{56} - 57q^{57} - 7q^{58} + 71q^{59} - 21q^{60} - 50q^{61} + 45q^{62} + 161q^{63} - 255q^{64} + 28q^{65} + 122q^{66} - 14q^{67} - 338q^{68} - 83q^{69} - 92q^{70} + 23q^{71} - 55q^{72} - 29q^{73} + 105q^{74} - 54q^{75} + 20q^{76} + 4q^{77} + 98q^{78} + 96q^{79} - 36q^{80} - 156q^{81} + 137q^{82} - 4q^{83} + 16q^{84} - 236q^{85} - 133q^{86} + 20q^{87} + 269q^{88} + 50q^{89} + 143q^{90} + 23q^{91} + 164q^{92} + 66q^{93} - 273q^{94} - 85q^{95} + 291q^{96} - 44q^{97} + 10q^{98} - 129q^{99} + O(q^{100})$$

## 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.v.a $$1008$$ $$3.777$$ None $$-21$$ $$-19$$ $$-19$$ $$-6$$