# Properties

 Label 5040.2.t Level $5040$ Weight $2$ Character orbit 5040.t Rep. character $\chi_{5040}(1009,\cdot)$ Character field $\Q$ Dimension $90$ Newform subspaces $28$ Sturm bound $2304$ Trace bound $19$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$5040 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5040.t (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$28$$ Sturm bound: $$2304$$ Trace bound: $$19$$ Distinguishing $$T_p$$: $$11$$, $$13$$, $$17$$, $$19$$, $$29$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(5040, [\chi])$$.

Total New Old
Modular forms 1200 90 1110
Cusp forms 1104 90 1014
Eisenstein series 96 0 96

## Trace form

 $$90 q + 2 q^{5} + O(q^{10})$$ $$90 q + 2 q^{5} + 12 q^{11} - 8 q^{19} + 2 q^{25} - 4 q^{29} + 8 q^{31} - 4 q^{41} - 90 q^{49} - 40 q^{55} - 12 q^{61} - 40 q^{71} - 28 q^{79} - 8 q^{85} + 20 q^{89} - 12 q^{91} + 32 q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(5040, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
5040.2.t.a $2$ $40.245$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+(-2+i)q^{5}-iq^{7}-q^{11}-iq^{13}+\cdots$$
5040.2.t.b $2$ $40.245$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+(-2-i)q^{5}-iq^{7}-4iq^{13}-2iq^{17}+\cdots$$
5040.2.t.c $2$ $40.245$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+(-2+i)q^{5}-iq^{7}+4iq^{13}+2iq^{17}+\cdots$$
5040.2.t.d $2$ $40.245$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+(-2-i)q^{5}+iq^{7}+4q^{11}+2iq^{13}+\cdots$$
5040.2.t.e $2$ $40.245$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-1+2i)q^{5}-iq^{7}-6q^{11}-2iq^{13}+\cdots$$
5040.2.t.f $2$ $40.245$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-1-2i)q^{5}+iq^{7}-2q^{11}-2iq^{13}+\cdots$$
5040.2.t.g $2$ $40.245$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-1-2i)q^{5}-iq^{7}-4iq^{13}-4iq^{17}+\cdots$$
5040.2.t.h $2$ $40.245$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-1-2i)q^{5}-iq^{7}+2q^{11}+6iq^{13}+\cdots$$
5040.2.t.i $2$ $40.245$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-1-2i)q^{5}-iq^{7}+6q^{11}+2iq^{13}+\cdots$$
5040.2.t.j $2$ $40.245$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(1+2i)q^{5}-iq^{7}-6q^{11}+2iq^{13}+\cdots$$
5040.2.t.k $2$ $40.245$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(1+2i)q^{5}+iq^{7}-2q^{11}+2iq^{13}+\cdots$$
5040.2.t.l $2$ $40.245$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(1-2i)q^{5}+iq^{7}+2q^{11}-2iq^{13}+\cdots$$
5040.2.t.m $2$ $40.245$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(1+2i)q^{5}+iq^{7}+2q^{11}-2iq^{13}+\cdots$$
5040.2.t.n $2$ $40.245$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(1+2i)q^{5}+iq^{7}+2q^{11}-2iq^{13}+\cdots$$
5040.2.t.o $2$ $40.245$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(2+i)q^{5}-iq^{7}-4q^{11}+6iq^{13}+\cdots$$
5040.2.t.p $2$ $40.245$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(2+i)q^{5}+iq^{7}-3q^{11}-iq^{13}+\cdots$$
5040.2.t.q $2$ $40.245$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(2-i)q^{5}+iq^{7}+4iq^{13}-2iq^{17}+\cdots$$
5040.2.t.r $2$ $40.245$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(2+i)q^{5}+iq^{7}-4iq^{13}+2iq^{17}+\cdots$$
5040.2.t.s $2$ $40.245$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(2-i)q^{5}+iq^{7}+3q^{11}+iq^{13}+\cdots$$
5040.2.t.t $4$ $40.245$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+(-1-\beta _{2}-\beta _{3})q^{5}+\beta _{2}q^{7}+(2\beta _{1}+\cdots)q^{11}+\cdots$$
5040.2.t.u $4$ $40.245$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{5}+\beta _{1}q^{7}-2q^{11}+2\beta _{2}q^{13}+\cdots$$
5040.2.t.v $6$ $40.245$ 6.0.350464.1 None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-\beta _{2}q^{5}+\beta _{1}q^{7}+2q^{11}+(2\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots$$
5040.2.t.w $6$ $40.245$ 6.0.350464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{5}+\beta _{1}q^{7}+(-2+\beta _{2}-\beta _{3}+\cdots)q^{11}+\cdots$$
5040.2.t.x $6$ $40.245$ 6.0.350464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{5}+\beta _{1}q^{7}+(2-\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{11}+\cdots$$
5040.2.t.y $6$ $40.245$ 6.0.5161984.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}+\beta _{5})q^{5}-\beta _{4}q^{7}+(2-\beta _{1}+\cdots)q^{11}+\cdots$$
5040.2.t.z $6$ $40.245$ 6.0.350464.1 None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\beta _{5}q^{5}+\beta _{1}q^{7}+(-\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{11}+\cdots$$
5040.2.t.ba $6$ $40.245$ 6.0.350464.1 None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\beta _{5}q^{5}-\beta _{1}q^{7}+(\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5})q^{11}+\cdots$$
5040.2.t.bb $8$ $40.245$ 8.0.49787136.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{7}q^{5}+\beta _{1}q^{7}+(\beta _{3}+\beta _{4}+\beta _{5}+\beta _{7})q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(5040, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(5040, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(90, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(120, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(180, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(210, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(240, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(280, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(315, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(360, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(420, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(560, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(630, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(720, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(840, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1260, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1680, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(2520, [\chi])$$$$^{\oplus 2}$$