# Properties

 Label 1350.2.r Level 1350 Weight 2 Character orbit r Rep. character $$\chi_{1350}(91,\cdot)$$ Character field $$\Q(\zeta_{15})$$ Dimension 240 Sturm bound 540

# Related objects

## Defining parameters

 Level: $$N$$ = $$1350 = 2 \cdot 3^{3} \cdot 5^{2}$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1350.r (of order $$15$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$225$$ Character field: $$\Q(\zeta_{15})$$ Sturm bound: $$540$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1350, [\chi])$$.

Total New Old
Modular forms 2256 240 2016
Cusp forms 2064 240 1824
Eisenstein series 192 0 192

## Trace form

 $$240q + 30q^{4} - 8q^{5} + O(q^{10})$$ $$240q + 30q^{4} - 8q^{5} - 4q^{11} - 8q^{14} + 30q^{16} - 24q^{17} + 2q^{20} + 24q^{25} - 96q^{26} - 12q^{29} - 12q^{31} - 8q^{35} + 24q^{37} + 12q^{38} - 16q^{41} + 8q^{44} - 26q^{47} - 120q^{49} + 12q^{50} + 72q^{53} - 8q^{56} + 12q^{58} - 18q^{59} + 36q^{62} - 60q^{64} + 104q^{65} + 18q^{67} - 48q^{68} - 24q^{70} - 4q^{71} + 80q^{74} - 32q^{77} + 12q^{79} - 4q^{80} - 48q^{82} + 104q^{83} + 12q^{85} - 20q^{86} + 188q^{89} - 8q^{95} + 12q^{97} - 48q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1350, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{2}^{\mathrm{old}}(1350, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1350, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(225, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(450, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(675, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database