# Properties

 Label 2100.2.q Level $2100$ Weight $2$ Character orbit 2100.q Rep. character $\chi_{2100}(1201,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $50$ Newform subspaces $13$ Sturm bound $960$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2100.q (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$13$$ Sturm bound: $$960$$ Trace bound: $$13$$ 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 50 982
Cusp forms 888 50 838
Eisenstein series 144 0 144

## Trace form

 $$50q + q^{3} + q^{7} - 25q^{9} + O(q^{10})$$ $$50q + q^{3} + q^{7} - 25q^{9} + 2q^{11} - 6q^{13} + 3q^{19} - 6q^{21} + 8q^{23} - 2q^{27} + 8q^{29} - 11q^{31} + 6q^{33} - 19q^{37} - q^{39} - 12q^{41} - 18q^{43} + 14q^{47} - 7q^{49} - 12q^{53} + 18q^{57} - 12q^{59} - 4q^{61} + 7q^{63} + 19q^{67} + 32q^{69} - 4q^{71} + 15q^{73} + 28q^{77} - 13q^{79} - 25q^{81} + 52q^{83} - 4q^{87} - 32q^{89} - 57q^{91} - 5q^{93} - 84q^{97} - 4q^{99} + O(q^{100})$$

## 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.q.a $$2$$ $$16.769$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$-5$$ $$q+(-1+\zeta_{6})q^{3}+(-2-\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots$$
2100.2.q.b $$2$$ $$16.769$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$-1$$ $$q+(-1+\zeta_{6})q^{3}+(-2+3\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots$$
2100.2.q.c $$2$$ $$16.769$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$4$$ $$q+(-1+\zeta_{6})q^{3}+(3-2\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots$$
2100.2.q.d $$2$$ $$16.769$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$5$$ $$q+(-1+\zeta_{6})q^{3}+(2+\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots$$
2100.2.q.e $$2$$ $$16.769$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$0$$ $$-4$$ $$q+(1-\zeta_{6})q^{3}+(-3+2\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots$$
2100.2.q.f $$4$$ $$16.769$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$-2$$ $$0$$ $$-2$$ $$q+(-1-\beta _{1})q^{3}+(-1-\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots$$
2100.2.q.g $$4$$ $$16.769$$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+(-1-\beta _{2})q^{3}-\beta _{1}q^{7}+\beta _{2}q^{9}+(3+\cdots)q^{11}+\cdots$$
2100.2.q.h $$4$$ $$16.769$$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+(1+\beta _{2})q^{3}+(-\beta _{1}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots$$
2100.2.q.i $$4$$ $$16.769$$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+(1+\beta _{2})q^{3}+\beta _{1}q^{7}+\beta _{2}q^{9}+(3+\beta _{1}+\cdots)q^{11}+\cdots$$
2100.2.q.j $$4$$ $$16.769$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$2$$ $$0$$ $$2$$ $$q+(1+\beta _{1})q^{3}+(1+\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots$$
2100.2.q.k $$4$$ $$16.769$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$2$$ $$0$$ $$2$$ $$q+(1+\beta _{1})q^{3}+(-\beta _{1}-\beta _{3})q^{7}+\beta _{1}q^{9}+\cdots$$
2100.2.q.l $$8$$ $$16.769$$ 8.0.$$\cdots$$.3 None $$0$$ $$-4$$ $$0$$ $$-2$$ $$q+\beta _{4}q^{3}+(-\beta _{1}+\beta _{6})q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots$$
2100.2.q.m $$8$$ $$16.769$$ 8.0.$$\cdots$$.3 None $$0$$ $$4$$ $$0$$ $$2$$ $$q-\beta _{4}q^{3}+(\beta _{1}-\beta _{6})q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(2100, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(210, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(350, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(420, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(525, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(700, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1050, [\chi])$$$$^{\oplus 2}$$