# Properties

 Label 403.2.bi Level 403 Weight 2 Character orbit bi Rep. character $$\chi_{403}(14,\cdot)$$ Character field $$\Q(\zeta_{15})$$ Dimension 256 Newforms 2 Sturm bound 74 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$403 = 13 \cdot 31$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 403.bi (of order $$15$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$31$$ Character field: $$\Q(\zeta_{15})$$ Newforms: $$2$$ Sturm bound: $$74$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

Total New Old
Modular forms 320 256 64
Cusp forms 288 256 32
Eisenstein series 32 0 32

## Trace form

 $$256q + 4q^{3} - 56q^{4} - 2q^{5} - 20q^{6} - 24q^{7} - 12q^{8} + 36q^{9} + O(q^{10})$$ $$256q + 4q^{3} - 56q^{4} - 2q^{5} - 20q^{6} - 24q^{7} - 12q^{8} + 36q^{9} + 10q^{10} + 8q^{11} + 16q^{12} + 2q^{13} - 6q^{14} - 22q^{15} - 80q^{16} - 6q^{17} - 48q^{19} - 2q^{20} + 2q^{21} + 26q^{22} + 10q^{23} + 92q^{24} - 114q^{25} - 24q^{26} - 32q^{27} - 6q^{28} + 32q^{29} + 32q^{30} + 136q^{32} + 22q^{33} + 36q^{34} + 20q^{35} - 148q^{36} + 20q^{37} - 18q^{38} + 66q^{40} - 22q^{41} - 122q^{42} - 14q^{43} - 18q^{44} - 128q^{45} - 56q^{46} - 72q^{47} - 82q^{48} - 34q^{49} - 42q^{50} + 10q^{51} + 6q^{52} - 44q^{53} + 108q^{54} + 46q^{55} - 12q^{56} - 48q^{57} + 112q^{58} - 18q^{59} + 200q^{60} - 20q^{61} + 32q^{62} + 24q^{63} - 136q^{64} + 2q^{65} + 100q^{66} - 38q^{67} + 68q^{68} - 62q^{69} - 94q^{70} + 30q^{71} - 12q^{72} - 116q^{74} + 60q^{75} - 28q^{76} + 76q^{77} + 14q^{79} + 72q^{80} + 90q^{81} - 22q^{82} - 30q^{83} - 250q^{84} - 56q^{85} - 66q^{86} + 40q^{87} + 98q^{88} - 62q^{89} + 158q^{90} - 16q^{91} + 32q^{92} + 44q^{93} - 76q^{94} + 90q^{95} - 52q^{96} + 22q^{97} + 78q^{98} - 60q^{99} + O(q^{100})$$

## 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.bi.a $$120$$ $$3.218$$ None $$6$$ $$2$$ $$13$$ $$-16$$
403.2.bi.b $$136$$ $$3.218$$ None $$-6$$ $$2$$ $$-15$$ $$-8$$

## Decomposition of $$S_{2}^{\mathrm{old}}(403, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(403, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(31, [\chi])$$$$^{\oplus 2}$$