# Properties

 Label 403.2.bg Level 403 Weight 2 Character orbit bg Rep. character $$\chi_{403}(123,\cdot)$$ Character field $$\Q(\zeta_{12})$$ Dimension 144 Newforms 1 Sturm bound 74 Trace bound 0

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## Defining parameters

 Level: $$N$$ = $$403 = 13 \cdot 31$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 403.bg (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$403$$ Character field: $$\Q(\zeta_{12})$$ 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 160 160 0
Cusp forms 144 144 0
Eisenstein series 16 16 0

## Trace form

 $$144q - 8q^{2} - 12q^{4} - 8q^{5} - 16q^{7} - 28q^{8} + 64q^{9} + O(q^{10})$$ $$144q - 8q^{2} - 12q^{4} - 8q^{5} - 16q^{7} - 28q^{8} + 64q^{9} - 12q^{10} + 68q^{16} - 52q^{18} - 4q^{19} - 44q^{20} - 64q^{28} - 4q^{31} - 28q^{32} + 36q^{33} + 28q^{35} - 12q^{36} - 28q^{39} - 48q^{40} - 8q^{41} + 12q^{45} - 24q^{47} + 48q^{49} + 40q^{50} + 48q^{56} + 8q^{59} + 42q^{62} - 84q^{63} - 80q^{66} + 4q^{67} - 24q^{69} - 96q^{70} - 80q^{71} + 104q^{72} - 116q^{76} + 24q^{78} - 112q^{80} + 16q^{81} + 108q^{82} - 92q^{87} + 64q^{93} + 4q^{94} - 132q^{95} + 120q^{97} - 160q^{98} + O(q^{100})$$

## 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.bg.a $$144$$ $$3.218$$ None $$-8$$ $$0$$ $$-8$$ $$-16$$