# Properties

 Label 2646.2.e Level $2646$ Weight $2$ Character orbit 2646.e Rep. character $\chi_{2646}(1549,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $80$ Newform subspaces $20$ Sturm bound $1008$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2646 = 2 \cdot 3^{3} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2646.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$63$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$20$$ Sturm bound: $$1008$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$5$$, $$11$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2646, [\chi])$$.

Total New Old
Modular forms 1104 80 1024
Cusp forms 912 80 832
Eisenstein series 192 0 192

## Trace form

 $$80 q + 80 q^{4} - 4 q^{5} + O(q^{10})$$ $$80 q + 80 q^{4} - 4 q^{5} + 8 q^{11} - 2 q^{13} + 80 q^{16} - 14 q^{17} + 4 q^{19} - 4 q^{20} + 2 q^{23} - 40 q^{25} - 16 q^{26} - 18 q^{29} + 4 q^{31} - 2 q^{37} - 12 q^{38} - 6 q^{41} - 2 q^{43} + 8 q^{44} + 6 q^{46} + 12 q^{47} - 2 q^{52} + 32 q^{53} + 12 q^{55} - 6 q^{58} + 44 q^{59} + 16 q^{61} + 44 q^{62} + 80 q^{64} - 4 q^{65} + 28 q^{67} - 14 q^{68} + 76 q^{71} + 28 q^{73} - 6 q^{74} + 4 q^{76} + 64 q^{79} - 4 q^{80} + 16 q^{83} - 24 q^{85} + 20 q^{86} - 36 q^{89} + 2 q^{92} + 24 q^{94} - 84 q^{95} - 2 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2646, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2646.2.e.a $$2$$ $$21.128$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$-1$$ $$0$$ $$q-q^{2}+q^{4}+(-1+\zeta_{6})q^{5}-q^{8}+(1+\cdots)q^{10}+\cdots$$
2646.2.e.b $$2$$ $$21.128$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+q^{4}-q^{8}-3\zeta_{6}q^{11}-2\zeta_{6}q^{13}+\cdots$$
2646.2.e.c $$2$$ $$21.128$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+q^{4}-q^{8}-3\zeta_{6}q^{11}+2\zeta_{6}q^{13}+\cdots$$
2646.2.e.d $$2$$ $$21.128$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$1$$ $$0$$ $$q-q^{2}+q^{4}+(1-\zeta_{6})q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots$$
2646.2.e.e $$2$$ $$21.128$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$3$$ $$0$$ $$q-q^{2}+q^{4}+(3-3\zeta_{6})q^{5}-q^{8}+(-3+\cdots)q^{10}+\cdots$$
2646.2.e.f $$2$$ $$21.128$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$-3$$ $$0$$ $$q+q^{2}+q^{4}+(-3+3\zeta_{6})q^{5}+q^{8}+\cdots$$
2646.2.e.g $$2$$ $$21.128$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$-3$$ $$0$$ $$q+q^{2}+q^{4}+(-3+3\zeta_{6})q^{5}+q^{8}+\cdots$$
2646.2.e.h $$2$$ $$21.128$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$-2$$ $$0$$ $$q+q^{2}+q^{4}+(-2+2\zeta_{6})q^{5}+q^{8}+\cdots$$
2646.2.e.i $$2$$ $$21.128$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$2$$ $$0$$ $$q+q^{2}+q^{4}+(2-2\zeta_{6})q^{5}+q^{8}+(2+\cdots)q^{10}+\cdots$$
2646.2.e.j $$2$$ $$21.128$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$3$$ $$0$$ $$q+q^{2}+q^{4}+(3-3\zeta_{6})q^{5}+q^{8}+(3+\cdots)q^{10}+\cdots$$
2646.2.e.k $$4$$ $$21.128$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$-4$$ $$0$$ $$-2$$ $$0$$ $$q-q^{2}+q^{4}+(-\beta _{1}+\beta _{2})q^{5}-q^{8}+\cdots$$
2646.2.e.l $$4$$ $$21.128$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$-4$$ $$0$$ $$2$$ $$0$$ $$q-q^{2}+q^{4}+(\beta _{1}-\beta _{2})q^{5}-q^{8}+(-\beta _{1}+\cdots)q^{10}+\cdots$$
2646.2.e.m $$4$$ $$21.128$$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$4$$ $$0$$ $$-3$$ $$0$$ $$q+q^{2}+q^{4}+(-\beta _{1}-\beta _{3})q^{5}+q^{8}+\cdots$$
2646.2.e.n $$4$$ $$21.128$$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$4$$ $$0$$ $$3$$ $$0$$ $$q+q^{2}+q^{4}+(\beta _{1}+\beta _{3})q^{5}+q^{8}+(\beta _{1}+\cdots)q^{10}+\cdots$$
2646.2.e.o $$6$$ $$21.128$$ 6.0.309123.1 None $$-6$$ $$0$$ $$-5$$ $$0$$ $$q-q^{2}+q^{4}+(-2+2\beta _{4}-\beta _{5})q^{5}+\cdots$$
2646.2.e.p $$6$$ $$21.128$$ 6.0.309123.1 None $$6$$ $$0$$ $$1$$ $$0$$ $$q+q^{2}+q^{4}+\beta _{2}q^{5}+q^{8}+\beta _{2}q^{10}+\cdots$$
2646.2.e.q $$8$$ $$21.128$$ $$\Q(\zeta_{24})$$ None $$-8$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+q^{4}-2\zeta_{24}^{7}q^{5}-q^{8}+2\zeta_{24}^{7}q^{10}+\cdots$$
2646.2.e.r $$8$$ $$21.128$$ 8.0.3317760000.3 None $$-8$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+q^{4}+\beta _{7}q^{5}-q^{8}-\beta _{7}q^{10}+\cdots$$
2646.2.e.s $$8$$ $$21.128$$ 8.0.$$\cdots$$.2 None $$8$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+q^{4}-\beta _{4}q^{5}+q^{8}-\beta _{4}q^{10}+\cdots$$
2646.2.e.t $$8$$ $$21.128$$ $$\Q(\zeta_{24})$$ None $$8$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+q^{4}-\zeta_{24}^{7}q^{5}+q^{8}-\zeta_{24}^{7}q^{10}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2646, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2646, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(189, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(378, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(441, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(882, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1323, [\chi])$$$$^{\oplus 2}$$