# Properties

 Label 1512.2.dc Level 1512 Weight 2 Character orbit dc Rep. character $$\chi_{1512}(169,\cdot)$$ Character field $$\Q(\zeta_{9})$$ Dimension 324 Sturm bound 576

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## Defining parameters

 Level: $$N$$ = $$1512 = 2^{3} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1512.dc (of order $$9$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$27$$ Character field: $$\Q(\zeta_{9})$$ Sturm bound: $$576$$

## Dimensions

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

Total New Old
Modular forms 1776 324 1452
Cusp forms 1680 324 1356
Eisenstein series 96 0 96

## Trace form

 $$324q + O(q^{10})$$ $$324q - 6q^{11} - 12q^{15} - 12q^{23} + 30q^{27} + 18q^{33} + 36q^{35} + 36q^{39} + 18q^{41} - 18q^{43} + 72q^{45} + 36q^{47} + 84q^{51} + 72q^{53} + 90q^{57} + 84q^{59} + 108q^{65} - 18q^{67} - 12q^{81} - 60q^{83} - 60q^{87} - 18q^{89} - 72q^{93} - 60q^{95} + 54q^{97} - 60q^{99} + O(q^{100})$$

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

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

## Decomposition of $$S_{2}^{\mathrm{old}}(1512, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1512, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(27, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(54, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(108, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(189, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(216, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(378, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(756, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database