# Properties

 Label 8100.2.d Level $8100$ Weight $2$ Character orbit 8100.d Rep. character $\chi_{8100}(649,\cdot)$ Character field $\Q$ Dimension $72$ Newform subspaces $19$ Sturm bound $3240$ Trace bound $29$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$8100 = 2^{2} \cdot 3^{4} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 8100.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$19$$ Sturm bound: $$3240$$ Trace bound: $$29$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$29$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(8100, [\chi])$$.

Total New Old
Modular forms 1728 72 1656
Cusp forms 1512 72 1440
Eisenstein series 216 0 216

## Trace form

 $$72 q + O(q^{10})$$ $$72 q + 12 q^{31} - 72 q^{49} + 36 q^{61} + 48 q^{79} - 72 q^{91} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(8100, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
8100.2.d.a $2$ $64.679$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{7}-6q^{11}-5iq^{13}-3iq^{17}+\cdots$$
8100.2.d.b $2$ $64.679$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{7}-3q^{11}-2iq^{13}-5q^{19}+\cdots$$
8100.2.d.c $2$ $64.679$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{7}-3q^{11}-iq^{13}+6iq^{17}+\cdots$$
8100.2.d.d $2$ $64.679$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{7}-3q^{11}+2iq^{13}-3iq^{17}+\cdots$$
8100.2.d.e $2$ $64.679$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{7}-4iq^{13}+6iq^{17}-2q^{19}+\cdots$$
8100.2.d.f $2$ $64.679$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{7}-4iq^{13}-6iq^{17}-2q^{19}+\cdots$$
8100.2.d.g $2$ $64.679$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{7}+3q^{11}-2iq^{13}-5q^{19}+\cdots$$
8100.2.d.h $2$ $64.679$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{7}+3q^{11}-iq^{13}-6iq^{17}+\cdots$$
8100.2.d.i $2$ $64.679$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{7}+3q^{11}+2iq^{13}+3iq^{17}+\cdots$$
8100.2.d.j $2$ $64.679$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{7}+6q^{11}-5iq^{13}+3iq^{17}+\cdots$$
8100.2.d.k $4$ $64.679$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{7}+(-2+\beta _{3})q^{11}+(2\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots$$
8100.2.d.l $4$ $64.679$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}^{3}q^{7}+\zeta_{12}q^{11}-2\zeta_{12}^{3}q^{13}+\cdots$$
8100.2.d.m $4$ $64.679$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}^{3}q^{7}-\zeta_{12}q^{11}-2\zeta_{12}^{3}q^{13}+\cdots$$
8100.2.d.n $4$ $64.679$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{7}+(2-\beta _{3})q^{11}+(2\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots$$
8100.2.d.o $6$ $64.679$ 6.0.5089536.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{3}+\beta _{4})q^{7}+\beta _{1}q^{11}+(-\beta _{3}-\beta _{5})q^{13}+\cdots$$
8100.2.d.p $6$ $64.679$ 6.0.5089536.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{3}+\beta _{4})q^{7}-\beta _{1}q^{11}+(-\beta _{3}-\beta _{5})q^{13}+\cdots$$
8100.2.d.q $8$ $64.679$ 8.0.4057180416.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{6}q^{7}+(-1-\beta _{1})q^{11}-\beta _{2}q^{13}+\cdots$$
8100.2.d.r $8$ $64.679$ 8.0.49787136.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{7}-\beta _{5}q^{11}-\beta _{1}q^{13}+\beta _{6}q^{17}+\cdots$$
8100.2.d.s $8$ $64.679$ 8.0.4057180416.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{6}q^{7}+(1+\beta _{1})q^{11}-\beta _{2}q^{13}+(2\beta _{3}+\cdots)q^{17}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(8100, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(8100, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(90, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(100, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(135, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(150, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(180, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(225, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(270, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(300, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(405, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(450, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(540, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(675, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(810, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(900, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1350, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1620, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(2025, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(2700, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(4050, [\chi])$$$$^{\oplus 2}$$