# Properties

 Label 403.2.bn Level 403 Weight 2 Character orbit bn Rep. character $$\chi_{403}(60,\cdot)$$ Character field $$\Q(\zeta_{20})$$ Dimension 272 Newforms 1 Sturm bound 74 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$403 = 13 \cdot 31$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 403.bn (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$403$$ Character field: $$\Q(\zeta_{20})$$ Newforms: $$1$$ 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 304 304 0
Cusp forms 272 272 0
Eisenstein series 32 32 0

## Trace form

 $$272q - 6q^{2} - 20q^{3} - 16q^{5} - 18q^{7} + 4q^{8} + 40q^{9} + O(q^{10})$$ $$272q - 6q^{2} - 20q^{3} - 16q^{5} - 18q^{7} + 4q^{8} + 40q^{9} + 8q^{14} - 40q^{15} + 20q^{16} + 16q^{18} + 14q^{19} - 4q^{20} + 50q^{21} - 120q^{22} - 50q^{24} + 40q^{27} + 46q^{28} - 20q^{29} - 14q^{31} + 52q^{32} - 70q^{33} - 10q^{34} + 20q^{35} - 46q^{39} - 44q^{40} - 20q^{41} - 20q^{42} + 30q^{44} - 36q^{45} - 50q^{46} + 26q^{47} - 20q^{48} + 30q^{50} - 50q^{52} + 50q^{54} - 20q^{55} - 100q^{58} + 2q^{59} - 40q^{60} - 4q^{63} - 172q^{66} + 12q^{67} - 102q^{70} + 50q^{71} - 18q^{72} - 10q^{73} - 20q^{74} + 148q^{76} + 66q^{78} - 100q^{79} - 120q^{80} + 88q^{81} - 40q^{83} - 70q^{84} - 10q^{86} - 88q^{87} - 20q^{89} + 150q^{91} + 48q^{93} - 24q^{94} + 40q^{96} - 76q^{97} - 8q^{98} + O(q^{100})$$

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

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
403.2.bn.a $$272$$ $$3.218$$ None $$-6$$ $$-20$$ $$-16$$ $$-18$$