# Properties

 Label 1152.4.d Level $1152$ Weight $4$ Character orbit 1152.d Rep. character $\chi_{1152}(577,\cdot)$ Character field $\Q$ Dimension $60$ Newform subspaces $17$ Sturm bound $768$ Trace bound $17$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1152 = 2^{7} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1152.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$17$$ Sturm bound: $$768$$ Trace bound: $$17$$ Distinguishing $$T_p$$: $$5$$, $$7$$, $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(1152, [\chi])$$.

Total New Old
Modular forms 608 60 548
Cusp forms 544 60 484
Eisenstein series 64 0 64

## Trace form

 $$60 q + O(q^{10})$$ $$60 q - 104 q^{17} - 1588 q^{25} - 392 q^{41} + 1500 q^{49} - 416 q^{65} + 24 q^{73} - 1960 q^{89} + 2008 q^{97} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(1152, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1152.4.d.a $2$ $67.970$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-64$$ $$q+3iq^{5}-2^{5}q^{7}-2iq^{11}-5iq^{13}+\cdots$$
1152.4.d.b $2$ $67.970$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-24$$ $$q+2iq^{5}-12q^{7}-3iq^{11}-5iq^{13}+\cdots$$
1152.4.d.c $2$ $67.970$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+11iq^{5}+46iq^{13}-104q^{17}-359q^{25}+\cdots$$
1152.4.d.d $2$ $67.970$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{5}-23iq^{13}-94q^{17}+109q^{25}+\cdots$$
1152.4.d.e $2$ $67.970$ $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{-2})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-5^{2}\beta q^{11}+90q^{17}+45\beta q^{19}+5^{3}q^{25}+\cdots$$
1152.4.d.f $2$ $67.970$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+11iq^{5}-46iq^{13}+104q^{17}-359q^{25}+\cdots$$
1152.4.d.g $2$ $67.970$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$24$$ $$q+2iq^{5}+12q^{7}+3iq^{11}-5iq^{13}+\cdots$$
1152.4.d.h $2$ $67.970$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$64$$ $$q+3iq^{5}+2^{5}q^{7}+2iq^{11}-5iq^{13}+\cdots$$
1152.4.d.i $4$ $67.970$ $$\Q(i, \sqrt{13})$$ None $$0$$ $$0$$ $$0$$ $$-32$$ $$q+(-\beta _{1}+\beta _{2})q^{5}+(-8+\beta _{3})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots$$
1152.4.d.j $4$ $67.970$ $$\Q(\sqrt{2}, \sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{5}+\beta _{2}q^{7}+7\beta _{1}q^{11}+\beta _{3}q^{13}+\cdots$$
1152.4.d.k $4$ $67.970$ $$\Q(i, \sqrt{7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3\beta _{1}q^{5}+\beta _{2}q^{7}+\beta _{3}q^{11}-10\beta _{1}q^{13}+\cdots$$
1152.4.d.l $4$ $67.970$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ $$\Q(\sqrt{-6})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{5}+\beta _{2}q^{7}+\beta _{1}q^{11}+17q^{25}+\cdots$$
1152.4.d.m $4$ $67.970$ $$\Q(i, \sqrt{7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3\beta _{1}q^{5}-\beta _{2}q^{7}-\beta _{3}q^{11}+10\beta _{1}q^{13}+\cdots$$
1152.4.d.n $4$ $67.970$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}^{2}q^{5}+5\zeta_{8}^{3}q^{7}-5\zeta_{8}q^{11}+14\zeta_{8}^{2}q^{13}+\cdots$$
1152.4.d.o $4$ $67.970$ $$\Q(i, \sqrt{13})$$ None $$0$$ $$0$$ $$0$$ $$32$$ $$q+(-\beta _{1}+\beta _{2})q^{5}+(8-\beta _{3})q^{7}+(-\beta _{1}+\cdots)q^{11}+\cdots$$
1152.4.d.p $8$ $67.970$ 8.0.1534132224.8 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{5}+\beta _{2}q^{7}+(\beta _{1}-\beta _{3})q^{11}+(\beta _{4}+\cdots)q^{13}+\cdots$$
1152.4.d.q $8$ $67.970$ 8.0.$$\cdots$$.260 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{5}+\beta _{2}q^{7}-\beta _{6}q^{11}-\beta _{3}q^{13}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(1152, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(1152, [\chi]) \simeq$$ $$S_{4}^{\mathrm{new}}(8, [\chi])$$$$^{\oplus 15}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(16, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(72, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(128, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(288, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(384, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(576, [\chi])$$$$^{\oplus 2}$$