# Properties

 Label 5184.2.f Level $5184$ Weight $2$ Character orbit 5184.f Rep. character $\chi_{5184}(2591,\cdot)$ Character field $\Q$ Dimension $96$ Newform subspaces $6$ Sturm bound $1728$ Trace bound $25$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$5184 = 2^{6} \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5184.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$24$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$1728$$ Trace bound: $$25$$ Distinguishing $$T_p$$: $$5$$, $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(5184, [\chi])$$.

Total New Old
Modular forms 936 96 840
Cusp forms 792 96 696
Eisenstein series 144 0 144

## Trace form

 $$96 q + O(q^{10})$$ $$96 q + 96 q^{25} - 96 q^{49} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(5184, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
5184.2.f.a $16$ $41.394$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$-12$$ $$0$$ $$q+(-1+\beta _{2})q^{5}+(\beta _{10}+\beta _{11})q^{7}+(-\beta _{7}+\cdots)q^{11}+\cdots$$
5184.2.f.b $16$ $41.394$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{5}+(\beta _{9}+\beta _{11})q^{7}+\beta _{14}q^{11}+\cdots$$
5184.2.f.c $16$ $41.394$ 16.0.$$\cdots$$.3 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{5}-\beta _{12}q^{7}+\beta _{1}q^{11}-\beta _{7}q^{13}+\cdots$$
5184.2.f.d $16$ $41.394$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{5}-\beta _{1}q^{7}+\beta _{11}q^{11}+\beta _{7}q^{13}+\cdots$$
5184.2.f.e $16$ $41.394$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{5}+(\beta _{9}+\beta _{11})q^{7}+\beta _{14}q^{11}+\cdots$$
5184.2.f.f $16$ $41.394$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$12$$ $$0$$ $$q+(1-\beta _{2})q^{5}+(-\beta _{10}-\beta _{11})q^{7}+(-\beta _{7}+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(5184, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(5184, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(72, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(216, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(288, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(576, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(648, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(864, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1728, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(2592, [\chi])$$$$^{\oplus 2}$$