# Properties

 Label 2760.2.da Level $2760$ Weight $2$ Character orbit 2760.da Rep. character $\chi_{2760}(131,\cdot)$ Character field $\Q(\zeta_{22})$ Dimension $3840$ Sturm bound $1152$

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## Defining parameters

 Level: $$N$$ $$=$$ $$2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2760.da (of order $$22$$ and degree $$10$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$552$$ Character field: $$\Q(\zeta_{22})$$ Sturm bound: $$1152$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2760, [\chi])$$.

Total New Old
Modular forms 5840 3840 2000
Cusp forms 5680 3840 1840
Eisenstein series 160 0 160

## Trace form

 $$3840q - 4q^{4} + 6q^{6} + O(q^{10})$$ $$3840q - 4q^{4} + 6q^{6} + 4q^{10} + 6q^{12} + 28q^{16} + 6q^{18} + 16q^{19} - 32q^{22} - 384q^{25} + 24q^{27} + 32q^{28} + 46q^{34} + 34q^{36} - 126q^{40} - 40q^{42} + 192q^{46} + 46q^{48} + 384q^{49} - 68q^{52} + 148q^{58} - 64q^{64} - 12q^{66} + 128q^{67} - 108q^{72} + 64q^{76} + 178q^{78} - 16q^{81} + 12q^{82} + 252q^{84} - 16q^{88} + 76q^{94} - 22q^{96} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2760, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{2}^{\mathrm{old}}(2760, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2760, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(552, [\chi])$$$$^{\oplus 2}$$