# Properties

 Label 3234.2.k Level 3234 Weight 2 Character orbit k Rep. character $$\chi_{3234}(815,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 264 Sturm bound 1344

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3234.k (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q(\zeta_{6})$$ Sturm bound: $$1344$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(3234, [\chi])$$.

Total New Old
Modular forms 1408 264 1144
Cusp forms 1280 264 1016
Eisenstein series 128 0 128

## Trace form

 $$264q + 132q^{4} - 4q^{9} + O(q^{10})$$ $$264q + 132q^{4} - 4q^{9} - 8q^{15} - 132q^{16} - 16q^{18} + 24q^{19} + 12q^{24} - 124q^{25} + 8q^{30} - 24q^{31} - 8q^{36} - 44q^{37} + 28q^{39} + 128q^{43} - 48q^{45} - 8q^{46} - 20q^{51} + 24q^{52} + 36q^{54} + 8q^{57} - 20q^{58} - 4q^{60} - 264q^{64} + 48q^{67} + 16q^{72} - 48q^{73} + 36q^{75} + 56q^{79} + 36q^{81} - 24q^{82} - 16q^{85} + 36q^{87} + 52q^{93} + 48q^{94} + 12q^{96} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(3234, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{2}^{\mathrm{old}}(3234, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(3234, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(147, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(231, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(294, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(462, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1617, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database