# Properties

 Label 4600.2.e Level $4600$ Weight $2$ Character orbit 4600.e Rep. character $\chi_{4600}(4049,\cdot)$ Character field $\Q$ Dimension $100$ Newform subspaces $23$ Sturm bound $1440$ Trace bound $19$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$4600 = 2^{3} \cdot 5^{2} \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 4600.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$23$$ Sturm bound: $$1440$$ Trace bound: $$19$$ Distinguishing $$T_p$$: $$3$$, $$7$$, $$11$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(4600, [\chi])$$.

Total New Old
Modular forms 744 100 644
Cusp forms 696 100 596
Eisenstein series 48 0 48

## Trace form

 $$100 q - 104 q^{9} + O(q^{10})$$ $$100 q - 104 q^{9} - 16 q^{29} + 8 q^{31} - 48 q^{39} + 20 q^{41} - 84 q^{49} + 84 q^{51} + 24 q^{59} - 20 q^{61} - 8 q^{69} + 40 q^{71} + 8 q^{79} + 116 q^{81} + 12 q^{89} - 24 q^{91} - 60 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(4600, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4600.2.e.a $2$ $36.731$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3iq^{3}+2iq^{7}-6q^{9}-5iq^{13}+\cdots$$
4600.2.e.b $2$ $36.731$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3iq^{3}-2iq^{7}-6q^{9}-iq^{13}+6q^{21}+\cdots$$
4600.2.e.c $2$ $36.731$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{3}+iq^{7}-q^{9}-5q^{11}-iq^{13}+\cdots$$
4600.2.e.d $2$ $36.731$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{3}+3iq^{7}-q^{9}+5q^{11}-5iq^{13}+\cdots$$
4600.2.e.e $2$ $36.731$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+2iq^{7}+2q^{9}-4q^{11}+5iq^{13}+\cdots$$
4600.2.e.f $2$ $36.731$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-4iq^{7}+2q^{9}-2q^{11}-7iq^{13}+\cdots$$
4600.2.e.g $2$ $36.731$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+2iq^{7}+2q^{9}+iq^{13}+4iq^{17}+\cdots$$
4600.2.e.h $2$ $36.731$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+2q^{9}+2q^{11}+5iq^{13}-4iq^{17}+\cdots$$
4600.2.e.i $2$ $36.731$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-4iq^{7}+2q^{9}+3q^{11}-2iq^{13}+\cdots$$
4600.2.e.j $2$ $36.731$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{7}+3q^{9}-6q^{11}+2iq^{13}-3iq^{17}+\cdots$$
4600.2.e.k $2$ $36.731$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+4iq^{7}+3q^{9}+6q^{11}+2iq^{13}+\cdots$$
4600.2.e.l $4$ $36.731$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}+\beta _{2})q^{3}+(-2\beta _{1}+\beta _{2})q^{7}+\cdots$$
4600.2.e.m $4$ $36.731$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-2\beta _{1}q^{7}+(-2+\beta _{3})q^{9}+\cdots$$
4600.2.e.n $4$ $36.731$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{3})q^{9}+\cdots$$
4600.2.e.o $4$ $36.731$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+(-2+\beta _{3})q^{9}+(2-2\beta _{3})q^{11}+\cdots$$
4600.2.e.p $6$ $36.731$ 6.0.431642176.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{7}+(-3+\beta _{3}+\cdots)q^{9}+\cdots$$
4600.2.e.q $6$ $36.731$ 6.0.3356224.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{3}-\beta _{5})q^{3}+(-2\beta _{3}-\beta _{5})q^{7}+(-1+\cdots)q^{9}+\cdots$$
4600.2.e.r $6$ $36.731$ 6.0.24681024.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots$$
4600.2.e.s $6$ $36.731$ 6.0.153664.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{3}+\beta _{5})q^{3}+(-2\beta _{3}-2\beta _{5})q^{7}+\cdots$$
4600.2.e.t $8$ $36.731$ 8.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{3}+(-\beta _{1}+\beta _{7})q^{7}+(-2+2\beta _{2}+\cdots)q^{9}+\cdots$$
4600.2.e.u $10$ $36.731$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+(-\beta _{6}+\beta _{8})q^{7}+(-2+\beta _{3}+\cdots)q^{9}+\cdots$$
4600.2.e.v $10$ $36.731$ 10.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{2}+\beta _{5})q^{3}+\beta _{8}q^{7}+(-2+\beta _{3}+\cdots)q^{9}+\cdots$$
4600.2.e.w $10$ $36.731$ 10.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+(-\beta _{4}+\beta _{6})q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(4600, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(4600, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(100, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(115, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(200, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(230, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(460, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(575, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(920, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1150, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(2300, [\chi])$$$$^{\oplus 2}$$