# Properties

 Label 403.2.cb Level 403 Weight 2 Character orbit cb Rep. character $$\chi_{403}(15,\cdot)$$ Character field $$\Q(\zeta_{60})$$ Dimension 576 Newform subspaces 1 Sturm bound 74 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$403 = 13 \cdot 31$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 403.cb (of order $$60$$ and degree $$16$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$403$$ Character field: $$\Q(\zeta_{60})$$ Newform subspaces: $$1$$ Sturm bound: $$74$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(403, [\chi])$$.

Total New Old
Modular forms 640 640 0
Cusp forms 576 576 0
Eisenstein series 64 64 0

## Trace form

 $$576q - 12q^{2} - 10q^{3} - 18q^{4} - 32q^{5} - 4q^{7} - 22q^{8} - 74q^{9} + O(q^{10})$$ $$576q - 12q^{2} - 10q^{3} - 18q^{4} - 32q^{5} - 4q^{7} - 22q^{8} - 74q^{9} - 18q^{10} - 30q^{13} - 80q^{14} + 10q^{15} - 78q^{16} - 30q^{17} + 2q^{18} - 16q^{19} + 34q^{20} - 70q^{21} - 60q^{22} - 30q^{23} + 20q^{24} + 80q^{27} - 16q^{28} - 10q^{29} + 24q^{31} - 112q^{32} + 4q^{33} - 20q^{34} - 38q^{35} - 48q^{36} + 28q^{39} + 8q^{40} - 22q^{41} - 10q^{42} - 120q^{43} - 60q^{44} + 18q^{45} - 100q^{46} + 4q^{47} - 10q^{48} - 78q^{49} - 120q^{50} + 20q^{52} - 80q^{54} - 10q^{55} + 432q^{56} + 70q^{58} + 52q^{59} + 160q^{60} - 72q^{62} - 316q^{63} - 30q^{65} + 40q^{66} - 44q^{67} + 174q^{69} + 66q^{70} - 20q^{71} - 264q^{72} - 20q^{73} - 10q^{74} + 210q^{75} + 26q^{76} + 96q^{78} + 40q^{79} - 18q^{80} + 54q^{81} - 138q^{82} - 290q^{83} + 220q^{84} - 30q^{85} - 20q^{86} - 8q^{87} - 10q^{89} + 70q^{91} - 134q^{93} - 24q^{94} + 102q^{95} - 70q^{96} - 110q^{97} + 200q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(403, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
403.2.cb.a $$576$$ $$3.218$$ None $$-12$$ $$-10$$ $$-32$$ $$-4$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database