# Properties

 Label 2760.2.k Level $2760$ Weight $2$ Character orbit 2760.k Rep. character $\chi_{2760}(2209,\cdot)$ Character field $\Q$ Dimension $68$ Newform subspaces $6$ Sturm bound $1152$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2760.k (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$1152$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

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

Total New Old
Modular forms 592 68 524
Cusp forms 560 68 492
Eisenstein series 32 0 32

## Trace form

 $$68q - 8q^{5} - 68q^{9} + O(q^{10})$$ $$68q - 8q^{5} - 68q^{9} - 4q^{15} - 4q^{25} + 32q^{29} + 8q^{31} - 32q^{41} + 8q^{45} - 60q^{49} - 8q^{55} - 32q^{61} + 16q^{65} - 8q^{69} - 40q^{79} + 68q^{81} + 24q^{85} + 48q^{89} + 48q^{91} + 24q^{95} + O(q^{100})$$

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

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2760.2.k.a $$2$$ $$22.039$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q-iq^{3}+(-2+i)q^{5}+2iq^{7}-q^{9}+\cdots$$
2760.2.k.b $$2$$ $$22.039$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-iq^{3}+(-1+2i)q^{5}-q^{9}+(2+i)q^{15}+\cdots$$
2760.2.k.c $$12$$ $$22.039$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{6}q^{3}-\beta _{10}q^{5}+\beta _{1}q^{7}-q^{9}+\beta _{2}q^{11}+\cdots$$
2760.2.k.d $$14$$ $$22.039$$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+\beta _{2}q^{3}-\beta _{12}q^{5}+(\beta _{2}+\beta _{10})q^{7}+\cdots$$
2760.2.k.e $$16$$ $$22.039$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\beta _{3}q^{3}-\beta _{5}q^{5}+\beta _{1}q^{7}-q^{9}+\beta _{14}q^{11}+\cdots$$
2760.2.k.f $$22$$ $$22.039$$ None $$0$$ $$0$$ $$-2$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(2760, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(115, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(120, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(230, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(345, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(460, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(690, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(920, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1380, [\chi])$$$$^{\oplus 2}$$