# Properties

 Label 2100.2.bc Level $2100$ Weight $2$ Character orbit 2100.bc Rep. character $\chi_{2100}(949,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $48$ Newform subspaces $8$ Sturm bound $960$ Trace bound $19$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2100.bc (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$8$$ Sturm bound: $$960$$ Trace bound: $$19$$ Distinguishing $$T_p$$: $$11$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2100, [\chi])$$.

Total New Old
Modular forms 1032 48 984
Cusp forms 888 48 840
Eisenstein series 144 0 144

## Trace form

 $$48 q + 24 q^{9} + O(q^{10})$$ $$48 q + 24 q^{9} + 12 q^{11} - 18 q^{19} - 2 q^{21} - 32 q^{29} - 16 q^{31} - 2 q^{39} - 72 q^{41} - 6 q^{49} - 8 q^{51} + 40 q^{59} + 46 q^{61} + 16 q^{69} + 80 q^{71} + 40 q^{79} - 24 q^{81} + 32 q^{89} + 2 q^{91} + 24 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2100, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2100.2.bc.a $4$ $16.769$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{3}+(-3\zeta_{12}+\zeta_{12}^{3})q^{7}+\zeta_{12}^{2}q^{9}+\cdots$$
2100.2.bc.b $4$ $16.769$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{3}+(-2\zeta_{12}-\zeta_{12}^{3})q^{7}+\zeta_{12}^{2}q^{9}+\cdots$$
2100.2.bc.c $4$ $16.769$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{3}+(-\zeta_{12}+3\zeta_{12}^{3})q^{7}+\zeta_{12}^{2}q^{9}+\cdots$$
2100.2.bc.d $4$ $16.769$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+(\zeta_{12}+2\zeta_{12}^{3})q^{7}+\cdots$$
2100.2.bc.e $8$ $16.769$ 8.0.49787136.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{3}+\beta _{1}q^{7}-\beta _{3}q^{9}+(-1-\beta _{3}+\cdots)q^{11}+\cdots$$
2100.2.bc.f $8$ $16.769$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}q^{3}+(-\zeta_{24}+\zeta_{24}^{3}-\zeta_{24}^{5}+\cdots)q^{7}+\cdots$$
2100.2.bc.g $8$ $16.769$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}q^{3}+(\zeta_{24}-\zeta_{24}^{5}+\zeta_{24}^{6})q^{7}+\cdots$$
2100.2.bc.h $8$ $16.769$ 8.0.49787136.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{3}-\beta _{6}q^{7}-\beta _{3}q^{9}+(3+3\beta _{3}+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2100, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2100, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(210, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(350, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(420, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(525, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(700, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1050, [\chi])$$$$^{\oplus 2}$$