# Properties

 Label 1512.2.du Level 1512 Weight 2 Character orbit du Rep. character $$\chi_{1512}(205,\cdot)$$ Character field $$\Q(\zeta_{18})$$ Dimension 1704 Sturm bound 576

# Related objects

## Defining parameters

 Level: $$N$$ = $$1512 = 2^{3} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1512.du (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$1512$$ Character field: $$\Q(\zeta_{18})$$ Sturm bound: $$576$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1512, [\chi])$$.

Total New Old
Modular forms 1752 1752 0
Cusp forms 1704 1704 0
Eisenstein series 48 48 0

## Trace form

 $$1704q - 3q^{2} - 3q^{4} - 12q^{6} - 12q^{7} - 6q^{8} - 6q^{9} + O(q^{10})$$ $$1704q - 3q^{2} - 3q^{4} - 12q^{6} - 12q^{7} - 6q^{8} - 6q^{9} + 3q^{10} - 3q^{12} + 24q^{14} - 24q^{15} - 3q^{16} + 6q^{17} - 3q^{18} - 12q^{20} - 12q^{22} - 6q^{23} - 54q^{24} - 6q^{25} - 6q^{26} - 12q^{28} - 21q^{30} - 6q^{31} + 57q^{32} - 6q^{33} - 18q^{34} + 18q^{36} - 75q^{38} - 6q^{39} - 33q^{40} - 24q^{41} + 9q^{42} - 6q^{44} - 6q^{46} - 6q^{47} - 78q^{48} - 12q^{49} + 3q^{50} - 3q^{52} - 45q^{54} - 48q^{55} - 27q^{56} - 6q^{57} - 3q^{58} - 63q^{60} + 27q^{62} - 72q^{63} - 6q^{64} - 6q^{65} - 3q^{66} + 36q^{68} + 9q^{70} - 12q^{71} + 87q^{72} - 12q^{73} + 63q^{74} - 30q^{78} - 6q^{79} - 6q^{80} - 6q^{81} - 6q^{82} + 75q^{84} - 9q^{86} - 6q^{87} + 21q^{88} + 6q^{89} - 39q^{90} - 72q^{92} - 3q^{94} - 66q^{95} - 219q^{96} - 24q^{97} + 54q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1512, [\chi])$$ into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database