# Properties

 Label 1152.2.d Level $1152$ Weight $2$ Character orbit 1152.d Rep. character $\chi_{1152}(577,\cdot)$ Character field $\Q$ Dimension $20$ Newform subspaces $8$ Sturm bound $384$ Trace bound $17$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1152 = 2^{7} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1152.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 $$M_{2}(1152, [\chi])$$.

Total New Old
Modular forms 224 20 204
Cusp forms 160 20 140
Eisenstein series 64 0 64

## Trace form

 $$20 q + O(q^{10})$$ $$20 q + 8 q^{17} - 28 q^{25} - 24 q^{41} + 52 q^{49} + 32 q^{65} - 56 q^{73} + 8 q^{89} + 72 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1152, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1152.2.d.a $2$ $9.199$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q-4q^{7}+iq^{11}-iq^{13}+2q^{17}-iq^{19}+\cdots$$
1152.2.d.b $2$ $9.199$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{5}+2iq^{13}-8q^{17}+q^{25}+5iq^{29}+\cdots$$
1152.2.d.c $2$ $9.199$ $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{-2})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta q^{11}-6q^{17}-3\beta q^{19}+5q^{25}+\cdots$$
1152.2.d.d $2$ $9.199$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{5}+iq^{13}+2q^{17}-11q^{25}+\cdots$$
1152.2.d.e $2$ $9.199$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{5}-2iq^{13}+8q^{17}+q^{25}+5iq^{29}+\cdots$$
1152.2.d.f $2$ $9.199$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q+4q^{7}+iq^{11}+iq^{13}+2q^{17}-iq^{19}+\cdots$$
1152.2.d.g $4$ $9.199$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ $$\Q(\sqrt{-6})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{5}+\beta _{1}q^{7}-\beta _{3}q^{11}-7q^{25}+\cdots$$
1152.2.d.h $4$ $9.199$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}^{2}q^{5}-\zeta_{8}^{3}q^{7}+\zeta_{8}q^{11}-2\zeta_{8}^{2}q^{13}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1152, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1152, [\chi]) \cong$$