# Properties

 Label 576.2.k Level $576$ Weight $2$ Character orbit 576.k Rep. character $\chi_{576}(145,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $18$ Newform subspaces $3$ Sturm bound $192$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$576 = 2^{6} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 576.k (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$16$$ Character field: $$\Q(i)$$ Newform subspaces: $$3$$ Sturm bound: $$192$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(576, [\chi])$$.

Total New Old
Modular forms 224 22 202
Cusp forms 160 18 142
Eisenstein series 64 4 60

## Trace form

 $$18 q + 2 q^{5} + O(q^{10})$$ $$18 q + 2 q^{5} - 6 q^{11} - 2 q^{13} + 4 q^{17} + 10 q^{19} + 10 q^{29} + 16 q^{31} + 20 q^{35} + 6 q^{37} + 22 q^{43} + 16 q^{47} - 10 q^{49} - 6 q^{53} + 26 q^{59} + 14 q^{61} + 12 q^{65} - 6 q^{67} - 20 q^{77} - 32 q^{79} - 42 q^{83} - 28 q^{85} - 52 q^{91} - 60 q^{95} - 4 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(576, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
576.2.k.a $2$ $4.599$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(1+i)q^{5}+2iq^{7}+(1+i)q^{11}+(-1+\cdots)q^{13}+\cdots$$
576.2.k.b $8$ $4.599$ 8.0.18939904.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{4}+\beta _{6})q^{5}+(\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{7}+\cdots$$
576.2.k.c $8$ $4.599$ 8.0.629407744.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{5}+(\beta _{3}-\beta _{7})q^{7}+(-\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(576, [\chi])$$ into lower level spaces

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