# Properties

 Label 576.4.d Level $576$ Weight $4$ Character orbit 576.d Rep. character $\chi_{576}(289,\cdot)$ Character field $\Q$ Dimension $30$ Newform subspaces $8$ Sturm bound $384$ Trace bound $17$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$576 = 2^{6} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 576.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$8$$ Sturm bound: $$384$$ Trace bound: $$17$$ Distinguishing $$T_p$$: $$5$$, $$7$$, $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(576, [\chi])$$.

Total New Old
Modular forms 312 30 282
Cusp forms 264 30 234
Eisenstein series 48 0 48

## Trace form

 $$30 q + O(q^{10})$$ $$30 q + 156 q^{17} - 618 q^{25} + 588 q^{41} + 750 q^{49} - 2304 q^{65} + 12 q^{73} + 2412 q^{89} + 3324 q^{97} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(576, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
576.4.d.a $2$ $33.985$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-2})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+9iq^{11}-90q^{17}-53iq^{19}+5^{3}q^{25}+\cdots$$
576.4.d.b $4$ $33.985$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-2\zeta_{12}^{2}q^{5}+\zeta_{12}q^{7}+6\zeta_{12}^{3}q^{11}+\cdots$$
576.4.d.c $4$ $33.985$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}^{2}q^{5}-7\zeta_{12}q^{7}+12\zeta_{12}^{3}q^{11}+\cdots$$
576.4.d.d $4$ $33.985$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}^{2}q^{7}+\zeta_{12}^{3}q^{13}-7\zeta_{12}q^{19}+\cdots$$
576.4.d.e $4$ $33.985$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}+21\zeta_{12}q^{11}+\cdots$$
576.4.d.f $4$ $33.985$ $$\Q(i, \sqrt{11})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{5}+\beta _{2}q^{7}+12\beta _{1}q^{11}-4\beta _{3}q^{13}+\cdots$$
576.4.d.g $4$ $33.985$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-3\zeta_{12}^{2}q^{5}+\zeta_{12}q^{7}+2^{4}\zeta_{12}^{2}q^{13}+\cdots$$
576.4.d.h $4$ $33.985$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-2\zeta_{12}^{2}q^{5}+\zeta_{12}q^{7}+6\zeta_{12}^{3}q^{11}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(576, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(576, [\chi]) \simeq$$ $$S_{4}^{\mathrm{new}}(8, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(16, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(72, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(288, [\chi])$$$$^{\oplus 2}$$