# Properties

 Label 403.2.bl Level 403 Weight 2 Character orbit bl Rep. character $$\chi_{403}(16,\cdot)$$ Character field $$\Q(\zeta_{15})$$ Dimension 288 Newform subspaces 2 Sturm bound 74 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$403 = 13 \cdot 31$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 403.bl (of order $$15$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$403$$ Character field: $$\Q(\zeta_{15})$$ Newform subspaces: $$2$$ 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 320 320 0
Cusp forms 288 288 0
Eisenstein series 32 32 0

## Trace form

 $$288q - 3q^{2} - 5q^{3} + 33q^{4} - 32q^{5} - 10q^{6} - 5q^{7} - 2q^{8} + 31q^{9} + O(q^{10})$$ $$288q - 3q^{2} - 5q^{3} + 33q^{4} - 32q^{5} - 10q^{6} - 5q^{7} - 2q^{8} + 31q^{9} - 9q^{10} - 6q^{11} + 14q^{12} - 5q^{13} - 48q^{14} - 12q^{15} + 45q^{16} - 3q^{17} + 6q^{18} - q^{19} + 15q^{20} + 38q^{21} - 34q^{22} - 18q^{23} + 43q^{24} + 232q^{25} - 6q^{26} - 68q^{27} + 3q^{28} - 23q^{29} - 36q^{30} - 60q^{31} - 26q^{32} - 25q^{33} - 136q^{34} - 28q^{35} - 152q^{36} - 26q^{37} + 16q^{38} + 18q^{39} - 116q^{40} + 13q^{41} + 31q^{42} - 28q^{43} + 12q^{44} - 52q^{45} - 15q^{46} - 20q^{47} - 11q^{48} + 45q^{49} - 21q^{50} - 104q^{51} + 62q^{52} + 16q^{53} + 49q^{54} - 40q^{55} - 78q^{56} + 140q^{57} + 31q^{58} - 19q^{59} - 52q^{60} + 34q^{61} + 3q^{62} - 122q^{63} - 102q^{64} + 17q^{65} + 16q^{66} + 6q^{67} + 86q^{68} - 67q^{69} - 22q^{70} + 41q^{71} + 47q^{72} - 56q^{73} - 9q^{74} - 4q^{75} - 34q^{76} + 40q^{77} - 72q^{78} + 80q^{79} - 114q^{80} - 29q^{81} + 45q^{82} - 134q^{83} + 81q^{84} - 54q^{85} + 212q^{86} - 38q^{87} + 82q^{88} + 21q^{89} - 26q^{90} + 46q^{91} - 336q^{92} - 30q^{93} - 18q^{94} + 34q^{95} + 186q^{96} + 13q^{97} + 88q^{98} - 60q^{99} + O(q^{100})$$

## 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.bl.a $$8$$ $$3.218$$ $$\Q(\zeta_{15})$$ None $$-4$$ $$-5$$ $$-24$$ $$-3$$ $$q+(-2+\zeta_{15}+\zeta_{15}^{2}-2\zeta_{15}^{3}+2\zeta_{15}^{4}+\cdots)q^{2}+\cdots$$
403.2.bl.b $$280$$ $$3.218$$ None $$1$$ $$0$$ $$-8$$ $$-2$$