# Properties

 Label 1152.2.k Level $1152$ Weight $2$ Character orbit 1152.k Rep. character $\chi_{1152}(289,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $36$ Newform subspaces $6$ Sturm bound $384$ Trace bound $19$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1152 = 2^{7} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1152.k (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$16$$ Character field: $$\Q(i)$$ Newform subspaces: $$6$$ Sturm bound: $$384$$ Trace bound: $$19$$ Distinguishing $$T_p$$: $$5$$, $$11$$, $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1152, [\chi])$$.

Total New Old
Modular forms 448 44 404
Cusp forms 320 36 284
Eisenstein series 128 8 120

## Trace form

 $$36 q - 4 q^{5} + O(q^{10})$$ $$36 q - 4 q^{5} + 4 q^{13} + 8 q^{17} - 20 q^{29} - 12 q^{37} - 20 q^{49} + 12 q^{53} - 28 q^{61} + 24 q^{65} + 40 q^{77} + 56 q^{85} - 8 q^{97} + O(q^{100})$$

## 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.k.a $2$ $9.199$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-1-i)q^{5}+2iq^{7}+(-1-i)q^{11}+\cdots$$
1152.2.k.b $2$ $9.199$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-1-i)q^{5}-2iq^{7}+(1+i)q^{11}+\cdots$$
1152.2.k.c $8$ $9.199$ 8.0.18939904.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{4}-\beta _{6})q^{5}+(-\beta _{1}-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots$$
1152.2.k.d $8$ $9.199$ 8.0.629407744.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{5}+(\beta _{3}-\beta _{7})q^{7}+(-\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$$
1152.2.k.e $8$ $9.199$ 8.0.629407744.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{5}+(-\beta _{3}+\beta _{7})q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots$$
1152.2.k.f $8$ $9.199$ 8.0.18939904.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{4}-\beta _{6})q^{5}+(\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(1152, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(16, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(128, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(288, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(384, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(576, [\chi])$$$$^{\oplus 2}$$