# Properties

 Label 3234.2.ba Level 3234 Weight 2 Character orbit ba Rep. character $$\chi_{3234}(419,\cdot)$$ Character field $$\Q(\zeta_{14})$$ Dimension 1104 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.ba (of order $$14$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$147$$ Character field: $$\Q(\zeta_{14})$$ Sturm bound: $$1344$$

## Dimensions

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

Total New Old
Modular forms 4080 1104 2976
Cusp forms 3984 1104 2880
Eisenstein series 96 0 96

## Trace form

 $$1104q + 184q^{4} + 28q^{6} - 12q^{7} + 20q^{9} + O(q^{10})$$ $$1104q + 184q^{4} + 28q^{6} - 12q^{7} + 20q^{9} - 24q^{15} - 184q^{16} + 4q^{21} - 168q^{25} + 12q^{28} - 16q^{30} - 20q^{36} + 108q^{37} + 24q^{39} - 84q^{42} - 40q^{43} + 120q^{46} + 24q^{51} + 84q^{52} - 60q^{57} + 20q^{58} + 24q^{60} + 308q^{61} + 28q^{63} + 184q^{64} + 72q^{67} + 32q^{70} + 168q^{75} + 56q^{79} - 20q^{81} + 80q^{84} + 128q^{85} + 84q^{90} + 8q^{91} - 20q^{93} + O(q^{100})$$

## 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

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

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database