# Properties

 Label 2880.3.l Level $2880$ Weight $3$ Character orbit 2880.l Rep. character $\chi_{2880}(1601,\cdot)$ Character field $\Q$ Dimension $64$ Newform subspaces $12$ Sturm bound $1728$ Trace bound $19$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2880 = 2^{6} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 2880.l (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$12$$ Sturm bound: $$1728$$ Trace bound: $$19$$ Distinguishing $$T_p$$: $$7$$, $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(2880, [\chi])$$.

Total New Old
Modular forms 1200 64 1136
Cusp forms 1104 64 1040
Eisenstein series 96 0 96

## Trace form

 $$64 q + O(q^{10})$$ $$64 q - 64 q^{13} - 320 q^{25} + 320 q^{37} + 448 q^{49} - 384 q^{61} - 320 q^{85} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(2880, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2880.3.l.a $4$ $78.474$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$-32$$ $$q-\beta _{2}q^{5}+(-8+\beta _{3})q^{7}+(\beta _{1}+6\beta _{2}+\cdots)q^{11}+\cdots$$
2880.3.l.b $4$ $78.474$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$-16$$ $$q+\beta _{2}q^{5}+(-4+\beta _{3})q^{7}+(-\beta _{1}+6\beta _{2}+\cdots)q^{11}+\cdots$$
2880.3.l.c $4$ $78.474$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$-16$$ $$q-\beta _{2}q^{5}+(-4-\beta _{3})q^{7}+(7\beta _{1}-2\beta _{2}+\cdots)q^{11}+\cdots$$
2880.3.l.d $4$ $78.474$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{5}-\beta _{3}q^{7}+(\beta _{1}-2\beta _{2})q^{11}+\cdots$$
2880.3.l.e $4$ $78.474$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{5}+\beta _{3}q^{7}+(-\beta _{1}+2\beta _{2})q^{11}+\cdots$$
2880.3.l.f $4$ $78.474$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$16$$ $$q+\beta _{2}q^{5}+(4-\beta _{3})q^{7}+(\beta _{1}-6\beta _{2})q^{11}+\cdots$$
2880.3.l.g $4$ $78.474$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$16$$ $$q-\beta _{2}q^{5}+(4+\beta _{3})q^{7}+(-7\beta _{1}+2\beta _{2}+\cdots)q^{11}+\cdots$$
2880.3.l.h $4$ $78.474$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$32$$ $$q-\beta _{2}q^{5}+(8+\beta _{3})q^{7}+(\beta _{1}-6\beta _{2})q^{11}+\cdots$$
2880.3.l.i $8$ $78.474$ 8.0.$$\cdots$$.9 None $$0$$ $$0$$ $$0$$ $$-16$$ $$q-\beta _{5}q^{5}+(-2-\beta _{1})q^{7}+(2\beta _{5}+\beta _{7})q^{11}+\cdots$$
2880.3.l.j $8$ $78.474$ 8.0.$$\cdots$$.4 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{5}-\beta _{5}q^{7}-\beta _{6}q^{11}+(-10+\cdots)q^{13}+\cdots$$
2880.3.l.k $8$ $78.474$ 8.0.$$\cdots$$.14 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{5}q^{5}+\beta _{1}q^{7}-\beta _{7}q^{11}+(6-\beta _{2}+\cdots)q^{13}+\cdots$$
2880.3.l.l $8$ $78.474$ 8.0.$$\cdots$$.9 None $$0$$ $$0$$ $$0$$ $$16$$ $$q-\beta _{5}q^{5}+(2-\beta _{1})q^{7}+(-2\beta _{5}+\beta _{7})q^{11}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(2880, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(2880, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 20}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(15, [\chi])$$$$^{\oplus 14}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 16}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 7}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(72, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(120, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(180, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(240, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(288, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(360, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(480, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(576, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(720, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(960, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(1440, [\chi])$$$$^{\oplus 2}$$