# Properties

 Label 1512.2.i Level 1512 Weight 2 Character orbit i Rep. character $$\chi_{1512}(1133,\cdot)$$ Character field $$\Q$$ Dimension 128 Sturm bound 576

# Related objects

## Defining parameters

 Level: $$N$$ = $$1512 = 2^{3} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1512.i (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$168$$ Character field: $$\Q$$ Sturm bound: $$576$$

## Dimensions

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

Total New Old
Modular forms 300 128 172
Cusp forms 276 128 148
Eisenstein series 24 0 24

## Trace form

 $$128q + O(q^{10})$$ $$128q - 16q^{16} + 4q^{22} - 128q^{25} - 2q^{28} + 4q^{46} + 8q^{49} + 20q^{58} - 48q^{64} - 42q^{70} - 64q^{79} + 20q^{88} + O(q^{100})$$

## 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

$$S_{2}^{\mathrm{old}}(1512, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(168, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(504, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database