# Properties

 Label 2880.2.k Level $2880$ Weight $2$ Character orbit 2880.k Rep. character $\chi_{2880}(1441,\cdot)$ Character field $\Q$ Dimension $40$ Newform subspaces $12$ Sturm bound $1152$ Trace bound $47$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2880 = 2^{6} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2880.k (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$12$$ Sturm bound: $$1152$$ Trace bound: $$47$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$23$$, $$47$$

## Dimensions

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

Total New Old
Modular forms 624 40 584
Cusp forms 528 40 488
Eisenstein series 96 0 96

## Trace form

 $$40 q + O(q^{10})$$ $$40 q - 40 q^{25} - 48 q^{41} + 8 q^{49} + 32 q^{73} + 48 q^{89} - 32 q^{97} + O(q^{100})$$

## 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.k.a $2$ $22.997$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q-iq^{5}-4q^{7}-4iq^{11}-2iq^{13}+\cdots$$
2880.2.k.b $2$ $22.997$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{5}+6iq^{13}+2iq^{19}-6q^{23}+\cdots$$
2880.2.k.c $2$ $22.997$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{5}-6iq^{13}+2iq^{19}+6q^{23}+\cdots$$
2880.2.k.d $2$ $22.997$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q+iq^{5}+4q^{7}-4iq^{11}+2iq^{13}+\cdots$$
2880.2.k.e $4$ $22.997$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$-12$$ $$q-\zeta_{12}q^{5}+(-3-\zeta_{12}^{3})q^{7}+2\zeta_{12}^{2}q^{11}+\cdots$$
2880.2.k.f $4$ $22.997$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q-\zeta_{12}q^{5}-2q^{7}+(-2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{11}+\cdots$$
2880.2.k.g $4$ $22.997$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{5}-\zeta_{12}^{3}q^{7}-\zeta_{12}^{2}q^{11}+\cdots$$
2880.2.k.h $4$ $22.997$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{5}-\zeta_{12}^{2}q^{11}-\zeta_{12}^{2}q^{13}+\cdots$$
2880.2.k.i $4$ $22.997$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{5}+\zeta_{12}^{2}q^{11}-\zeta_{12}^{2}q^{13}+\cdots$$
2880.2.k.j $4$ $22.997$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{5}-\zeta_{12}^{3}q^{7}-\zeta_{12}^{2}q^{11}+\cdots$$
2880.2.k.k $4$ $22.997$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q-\zeta_{12}q^{5}+2q^{7}+(2\zeta_{12}-\zeta_{12}^{2})q^{11}+\cdots$$
2880.2.k.l $4$ $22.997$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$12$$ $$q-\zeta_{12}q^{5}+(3+\zeta_{12}^{3})q^{7}-2\zeta_{12}^{2}q^{11}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(2880, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(72, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(120, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(160, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(288, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(320, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(360, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(480, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(576, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(960, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1440, [\chi])$$$$^{\oplus 2}$$