# Properties

 Label 1344.4.bw Level $1344$ Weight $4$ Character orbit 1344.bw Rep. character $\chi_{1344}(17,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $752$ Sturm bound $1024$

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## Defining parameters

 Level: $$N$$ $$=$$ $$1344 = 2^{6} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1344.bw (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$336$$ Character field: $$\Q(\zeta_{12})$$ Sturm bound: $$1024$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(1344, [\chi])$$.

Total New Old
Modular forms 3136 784 2352
Cusp forms 3008 752 2256
Eisenstein series 128 32 96

## Trace form

 $$752q + 6q^{3} + O(q^{10})$$ $$752q + 6q^{3} + 16q^{15} + 12q^{19} + 50q^{21} + 24q^{31} - 12q^{33} - 4q^{37} + 16q^{43} - 6q^{45} - 16q^{49} - 806q^{51} - 12q^{61} + 1380q^{63} - 1628q^{67} - 744q^{75} + 8q^{79} - 4q^{81} + 984q^{85} + 952q^{91} - 110q^{93} - 2908q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(1344, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{4}^{\mathrm{old}}(1344, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(1344, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(336, [\chi])$$$$^{\oplus 3}$$