# Properties

 Label 2880.2.t Level $2880$ Weight $2$ Character orbit 2880.t Rep. character $\chi_{2880}(721,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $80$ Newform subspaces $5$ Sturm bound $1152$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2880 = 2^{6} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2880.t (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$16$$ Character field: $$\Q(i)$$ Newform subspaces: $$5$$ Sturm bound: $$1152$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

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

Total New Old
Modular forms 1216 80 1136
Cusp forms 1088 80 1008
Eisenstein series 128 0 128

## Trace form

 $$80q + O(q^{10})$$ $$80q + 8q^{11} - 8q^{19} - 16q^{29} - 16q^{37} - 8q^{43} - 40q^{47} - 80q^{49} + 16q^{53} - 40q^{59} - 16q^{61} - 8q^{67} + 16q^{77} + 16q^{79} + 40q^{83} + 16q^{85} + 64q^{91} + 32q^{95} + O(q^{100})$$

## 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.t.a $$4$$ $$22.997$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{5}+(2\zeta_{8}+2\zeta_{8}^{2}+2\zeta_{8}^{3})q^{7}+\cdots$$
2880.2.t.b $$8$$ $$22.997$$ 8.0.18939904.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{5}+(\beta _{2}+\beta _{3})q^{7}+(1+\beta _{1}-\beta _{3}+\cdots)q^{11}+\cdots$$
2880.2.t.c $$16$$ $$22.997$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{5}q^{5}+(-\beta _{1}+\beta _{4}+\beta _{7}-\beta _{8}-\beta _{10}+\cdots)q^{7}+\cdots$$
2880.2.t.d $$20$$ $$22.997$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{5}q^{5}-\beta _{13}q^{7}+(-\beta _{5}+\beta _{8})q^{11}+\cdots$$
2880.2.t.e $$32$$ $$22.997$$ None $$0$$ $$0$$ $$0$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(2880, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(16, [\chi])$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(240, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(320, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(576, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(720, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(960, [\chi])$$$$^{\oplus 2}$$