# Properties

 Label 2880.2.h Level $2880$ Weight $2$ Character orbit 2880.h Rep. character $\chi_{2880}(1151,\cdot)$ Character field $\Q$ Dimension $32$ Newform subspaces $6$ Sturm bound $1152$ Trace bound $23$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2880 = 2^{6} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2880.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$12$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$1152$$ Trace bound: $$23$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$23$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2880, [\chi])$$.

Total New Old
Modular forms 624 32 592
Cusp forms 528 32 496
Eisenstein series 96 0 96

## Trace form

 $$32q + O(q^{10})$$ $$32q + 32q^{13} - 32q^{25} - 32q^{37} - 32q^{49} - 64q^{61} + 32q^{85} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2880, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2880.2.h.a $$4$$ $$22.997$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}q^{5}+(2\zeta_{8}-\zeta_{8}^{2})q^{7}+(-4-\zeta_{8}^{3})q^{11}+\cdots$$
2880.2.h.b $$4$$ $$22.997$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{5}+(2\zeta_{8}-\zeta_{8}^{2})q^{7}+\zeta_{8}^{3}q^{11}+\cdots$$
2880.2.h.c $$4$$ $$22.997$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}q^{5}+(2\zeta_{8}-\zeta_{8}^{2})q^{7}-\zeta_{8}^{3}q^{11}+\cdots$$
2880.2.h.d $$4$$ $$22.997$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{5}+(2\zeta_{8}-\zeta_{8}^{2})q^{7}+(4+\zeta_{8}^{3})q^{11}+\cdots$$
2880.2.h.e $$8$$ $$22.997$$ 8.0.18939904.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{5}-\beta _{7}q^{7}+\beta _{1}q^{11}+(-2-\beta _{2}+\cdots)q^{13}+\cdots$$
2880.2.h.f $$8$$ $$22.997$$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}q^{5}+\zeta_{24}^{5}q^{7}+(\zeta_{24}^{2}-\zeta_{24}^{4}+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2880, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2880, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(180, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(240, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(288, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(480, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(576, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(720, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(960, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1440, [\chi])$$$$^{\oplus 2}$$