# Properties

 Label 1350.2.bc Level 1350 Weight 2 Character orbit bc Rep. character $$\chi_{1350}(31,\cdot)$$ Character field $$\Q(\zeta_{45})$$ Dimension 2160 Sturm bound 540

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## Defining parameters

 Level: $$N$$ = $$1350 = 2 \cdot 3^{3} \cdot 5^{2}$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1350.bc (of order $$45$$ and degree $$24$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$675$$ Character field: $$\Q(\zeta_{45})$$ Sturm bound: $$540$$

## Dimensions

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

Total New Old
Modular forms 6576 2160 4416
Cusp forms 6384 2160 4224
Eisenstein series 192 0 192

## Trace form

 $$2160q - 24q^{5} + O(q^{10})$$ $$2160q - 24q^{5} - 42q^{15} - 12q^{20} - 72q^{21} + 24q^{23} - 72q^{25} + 288q^{26} + 12q^{27} - 36q^{30} + 36q^{31} + 12q^{33} - 18q^{35} - 24q^{36} + 36q^{38} + 60q^{39} + 48q^{42} + 12q^{44} + 174q^{45} - 78q^{47} - 18q^{48} + 36q^{50} + 120q^{53} + 36q^{54} + 36q^{57} - 18q^{59} + 18q^{60} + 84q^{63} + 270q^{64} + 18q^{65} + 108q^{67} - 144q^{68} - 48q^{72} + 48q^{75} + 336q^{77} + 24q^{78} - 36q^{81} + 60q^{83} - 282q^{87} + 12q^{89} + 30q^{90} + 72q^{92} + 48q^{93} + 42q^{95} - 72q^{97} + 60q^{99} + O(q^{100})$$

## 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

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

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database