# Properties

 Label 5400.2.f Level $5400$ Weight $2$ Character orbit 5400.f Rep. character $\chi_{5400}(649,\cdot)$ Character field $\Q$ Dimension $72$ Newform subspaces $32$ Sturm bound $2160$ Trace bound $29$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$5400 = 2^{3} \cdot 3^{3} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5400.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$32$$ Sturm bound: $$2160$$ Trace bound: $$29$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$13$$, $$29$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(5400, [\chi])$$.

Total New Old
Modular forms 1152 72 1080
Cusp forms 1008 72 936
Eisenstein series 144 0 144

## Trace form

 $$72 q + O(q^{10})$$ $$72 q + 4 q^{31} - 84 q^{49} - 48 q^{61} - 52 q^{79} - 68 q^{91} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(5400, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
5400.2.f.a $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{7}-6q^{11}-6iq^{13}-2iq^{17}+\cdots$$
5400.2.f.b $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3iq^{7}-5q^{11}-4iq^{13}+8iq^{17}+\cdots$$
5400.2.f.c $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{7}-5q^{11}-iq^{13}+2iq^{17}+\cdots$$
5400.2.f.d $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3iq^{7}-4q^{11}+6iq^{13}+6iq^{17}+\cdots$$
5400.2.f.e $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3iq^{7}-4q^{11}+iq^{13}-4iq^{17}+\cdots$$
5400.2.f.f $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{7}-4q^{11}+2iq^{13}-5iq^{17}+\cdots$$
5400.2.f.g $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+4iq^{7}-4q^{11}+iq^{13}+8iq^{17}+\cdots$$
5400.2.f.h $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{7}-3q^{11}-3iq^{13}-2iq^{17}+\cdots$$
5400.2.f.i $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{7}-2q^{11}-2iq^{13}-2iq^{17}+\cdots$$
5400.2.f.j $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-2q^{11}-3iq^{17}+q^{19}+3iq^{23}+\cdots$$
5400.2.f.k $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{7}-2q^{11}-5iq^{13}+4iq^{17}+\cdots$$
5400.2.f.l $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+4iq^{7}-2q^{11}+4iq^{13}+iq^{17}+\cdots$$
5400.2.f.m $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{7}-q^{11}-iq^{13}+iq^{17}-4q^{19}+\cdots$$
5400.2.f.n $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{7}-6iq^{13}-7iq^{17}-7q^{19}+\cdots$$
5400.2.f.o $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{7}-6iq^{13}+7iq^{17}-7q^{19}+\cdots$$
5400.2.f.p $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{7}+q^{11}-iq^{13}-iq^{17}-4q^{19}+\cdots$$
5400.2.f.q $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{7}+2q^{11}-2iq^{13}+2iq^{17}+\cdots$$
5400.2.f.r $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2q^{11}-3iq^{17}+q^{19}+3iq^{23}+\cdots$$
5400.2.f.s $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+4iq^{7}+2q^{11}+4iq^{13}-iq^{17}+\cdots$$
5400.2.f.t $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{7}+2q^{11}-5iq^{13}-4iq^{17}+\cdots$$
5400.2.f.u $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{7}+3q^{11}-3iq^{13}+2iq^{17}+\cdots$$
5400.2.f.v $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3iq^{7}+4q^{11}+iq^{13}+4iq^{17}+\cdots$$
5400.2.f.w $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3iq^{7}+4q^{11}+6iq^{13}-6iq^{17}+\cdots$$
5400.2.f.x $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{7}+4q^{11}+2iq^{13}+5iq^{17}+\cdots$$
5400.2.f.y $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+4iq^{7}+4q^{11}+iq^{13}-8iq^{17}+\cdots$$
5400.2.f.z $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3iq^{7}+5q^{11}-4iq^{13}-8iq^{17}+\cdots$$
5400.2.f.ba $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{7}+5q^{11}-iq^{13}-2iq^{17}+\cdots$$
5400.2.f.bb $2$ $43.119$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{7}+6q^{11}-6iq^{13}+2iq^{17}+\cdots$$
5400.2.f.bc $4$ $43.119$ $$\Q(i, \sqrt{13})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}+\beta _{2})q^{7}-q^{11}+(2\beta _{1}+\beta _{2}+\cdots)q^{13}+\cdots$$
5400.2.f.bd $4$ $43.119$ $$\Q(i, \sqrt{73})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{7}-\beta _{3}q^{11}+3\beta _{2}q^{13}+(-\beta _{1}+\cdots)q^{17}+\cdots$$
5400.2.f.be $4$ $43.119$ $$\Q(i, \sqrt{73})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{7}+\beta _{3}q^{11}+3\beta _{2}q^{13}+(\beta _{1}+\cdots)q^{17}+\cdots$$
5400.2.f.bf $4$ $43.119$ $$\Q(i, \sqrt{13})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}+\beta _{2})q^{7}+q^{11}+(2\beta _{1}+\beta _{2}+\cdots)q^{13}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(5400, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(5400, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(90, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(100, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(120, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(135, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(150, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(180, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(200, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(225, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(270, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(300, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(360, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(450, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(540, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(600, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(675, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(900, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1080, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1350, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1800, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(2700, [\chi])$$$$^{\oplus 2}$$