# Properties

 Label 1280.4.d Level $1280$ Weight $4$ Character orbit 1280.d Rep. character $\chi_{1280}(641,\cdot)$ Character field $\Q$ Dimension $96$ Newform subspaces $29$ Sturm bound $768$ Trace bound $15$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1280 = 2^{8} \cdot 5$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1280.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$29$$ Sturm bound: $$768$$ Trace bound: $$15$$ Distinguishing $$T_p$$: $$3$$, $$7$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(1280, [\chi])$$.

Total New Old
Modular forms 600 96 504
Cusp forms 552 96 456
Eisenstein series 48 0 48

## Trace form

 $$96 q - 864 q^{9} + O(q^{10})$$ $$96 q - 864 q^{9} - 2400 q^{25} + 7584 q^{49} - 1344 q^{57} + 1728 q^{73} + 7776 q^{81} - 6336 q^{97} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(1280, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1280.4.d.a $2$ $75.522$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-68$$ $$q+6iq^{3}+5iq^{5}-34q^{7}-9q^{9}+2^{4}iq^{11}+\cdots$$
1280.4.d.b $2$ $75.522$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-36$$ $$q+10iq^{3}-5iq^{5}-18q^{7}-73q^{9}+\cdots$$
1280.4.d.c $2$ $75.522$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-32$$ $$q+4iq^{3}+5iq^{5}-2^{4}q^{7}+11q^{9}+\cdots$$
1280.4.d.d $2$ $75.522$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-32$$ $$q+4iq^{3}-5iq^{5}-2^{4}q^{7}+11q^{9}+\cdots$$
1280.4.d.e $2$ $75.522$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-12$$ $$q+2iq^{3}+5iq^{5}-6q^{7}+23q^{9}-2^{5}iq^{11}+\cdots$$
1280.4.d.f $2$ $75.522$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-12$$ $$q+2iq^{3}-5iq^{5}-6q^{7}+23q^{9}+60iq^{11}+\cdots$$
1280.4.d.g $2$ $75.522$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+8iq^{3}-5iq^{5}-4q^{7}-37q^{9}+12iq^{11}+\cdots$$
1280.4.d.h $2$ $75.522$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+8iq^{3}-5iq^{5}-2q^{7}-37q^{9}-22iq^{11}+\cdots$$
1280.4.d.i $2$ $75.522$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+8iq^{3}+5iq^{5}+2q^{7}-37q^{9}-22iq^{11}+\cdots$$
1280.4.d.j $2$ $75.522$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q+8iq^{3}+5iq^{5}+4q^{7}-37q^{9}+12iq^{11}+\cdots$$
1280.4.d.k $2$ $75.522$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$12$$ $$q+2iq^{3}+5iq^{5}+6q^{7}+23q^{9}+60iq^{11}+\cdots$$
1280.4.d.l $2$ $75.522$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$12$$ $$q+2iq^{3}-5iq^{5}+6q^{7}+23q^{9}-2^{5}iq^{11}+\cdots$$
1280.4.d.m $2$ $75.522$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$32$$ $$q+4iq^{3}+5iq^{5}+2^{4}q^{7}+11q^{9}+\cdots$$
1280.4.d.n $2$ $75.522$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$32$$ $$q+4iq^{3}-5iq^{5}+2^{4}q^{7}+11q^{9}+\cdots$$
1280.4.d.o $2$ $75.522$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$36$$ $$q+10iq^{3}+5iq^{5}+18q^{7}-73q^{9}+\cdots$$
1280.4.d.p $2$ $75.522$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$68$$ $$q+6iq^{3}-5iq^{5}+34q^{7}-9q^{9}+2^{4}iq^{11}+\cdots$$
1280.4.d.q $4$ $75.522$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$0$$ $$-16$$ $$q+(4\beta _{1}-\beta _{2})q^{3}-5\beta _{1}q^{5}+(-4-5\beta _{3})q^{7}+\cdots$$
1280.4.d.r $4$ $75.522$ $$\Q(i, \sqrt{51})$$ None $$0$$ $$0$$ $$0$$ $$-16$$ $$q+2\beta _{1}q^{3}-5\beta _{1}q^{5}+(-4+\beta _{2})q^{7}+\cdots$$
1280.4.d.s $4$ $75.522$ $$\Q(i, \sqrt{21})$$ None $$0$$ $$0$$ $$0$$ $$-12$$ $$q+(-\beta _{1}+\beta _{2})q^{3}+5\beta _{1}q^{5}+(-3-3\beta _{3})q^{7}+\cdots$$
1280.4.d.t $4$ $75.522$ $$\Q(i, \sqrt{13})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{3}+5\beta _{1}q^{5}+\beta _{3}q^{7}-5^{2}q^{9}+\cdots$$
1280.4.d.u $4$ $75.522$ $$\Q(i, \sqrt{10})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}-5\beta _{1}q^{5}-3\beta _{3}q^{7}-13q^{9}+\cdots$$
1280.4.d.v $4$ $75.522$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{3}+5\beta _{1}q^{5}-7\beta _{3}q^{7}+7q^{9}+\cdots$$
1280.4.d.w $4$ $75.522$ $$\Q(i, \sqrt{21})$$ None $$0$$ $$0$$ $$0$$ $$12$$ $$q+(-\beta _{1}+\beta _{2})q^{3}-5\beta _{1}q^{5}+(3+3\beta _{3})q^{7}+\cdots$$
1280.4.d.x $4$ $75.522$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$0$$ $$16$$ $$q+(4\beta _{1}-\beta _{2})q^{3}+5\beta _{1}q^{5}+(4+5\beta _{3})q^{7}+\cdots$$
1280.4.d.y $4$ $75.522$ $$\Q(i, \sqrt{51})$$ None $$0$$ $$0$$ $$0$$ $$16$$ $$q+2\beta _{1}q^{3}+5\beta _{1}q^{5}+(4-\beta _{2})q^{7}+23q^{9}+\cdots$$
1280.4.d.z $6$ $75.522$ 6.0.12559936.1 None $$0$$ $$0$$ $$0$$ $$-40$$ $$q+(-\beta _{2}+\beta _{4})q^{3}+5\beta _{2}q^{5}+(-7-\beta _{1}+\cdots)q^{7}+\cdots$$
1280.4.d.ba $6$ $75.522$ 6.0.12559936.1 None $$0$$ $$0$$ $$0$$ $$40$$ $$q+(-\beta _{2}+\beta _{4})q^{3}-5\beta _{2}q^{5}+(7+\beta _{1}+\cdots)q^{7}+\cdots$$
1280.4.d.bb $8$ $75.522$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-40$$ $$q+(\beta _{1}-\beta _{5})q^{3}+5\beta _{1}q^{5}+(-5+\beta _{2}+\cdots)q^{7}+\cdots$$
1280.4.d.bc $8$ $75.522$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$40$$ $$q+(\beta _{1}-\beta _{5})q^{3}-5\beta _{1}q^{5}+(5-\beta _{2})q^{7}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(1280, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(1280, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(8, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(128, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(160, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(256, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(320, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(640, [\chi])$$$$^{\oplus 2}$$