# Properties

 Label 1014.2.i Level $1014$ Weight $2$ Character orbit 1014.i Rep. character $\chi_{1014}(361,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $48$ Newform subspaces $8$ Sturm bound $364$ Trace bound $10$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1014 = 2 \cdot 3 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1014.i (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$8$$ Sturm bound: $$364$$ Trace bound: $$10$$ Distinguishing $$T_p$$: $$5$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1014, [\chi])$$.

Total New Old
Modular forms 420 48 372
Cusp forms 308 48 260
Eisenstein series 112 0 112

## Trace form

 $$48q + 24q^{4} - 24q^{9} + O(q^{10})$$ $$48q + 24q^{4} - 24q^{9} - 4q^{10} + 24q^{14} + 12q^{15} - 24q^{16} + 12q^{17} - 4q^{22} + 16q^{23} - 72q^{25} - 20q^{29} - 4q^{30} - 12q^{33} - 24q^{35} + 24q^{36} + 12q^{37} - 8q^{38} - 8q^{40} - 48q^{41} + 4q^{42} + 8q^{43} + 36q^{49} - 24q^{50} - 32q^{51} + 24q^{53} - 8q^{55} + 12q^{56} + 12q^{58} + 48q^{59} + 20q^{62} - 48q^{64} - 24q^{66} + 48q^{67} - 12q^{68} + 4q^{69} - 24q^{71} + 8q^{74} - 8q^{75} + 32q^{77} + 72q^{79} - 24q^{81} + 8q^{82} + 12q^{84} - 36q^{85} + 4q^{88} + 24q^{89} + 8q^{90} + 32q^{92} + 24q^{93} - 8q^{94} - 8q^{95} - 24q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1014, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1014.2.i.a $$4$$ $$8.097$$ $$\Q(\zeta_{12})$$ None $$0$$ $$-2$$ $$0$$ $$-6$$ $$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}-\zeta_{12}^{2}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots$$
1014.2.i.b $$4$$ $$8.097$$ $$\Q(\zeta_{12})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}-\zeta_{12}^{2}q^{3}+(1+\cdots)q^{4}+\cdots$$
1014.2.i.c $$4$$ $$8.097$$ $$\Q(\zeta_{12})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}-\zeta_{12}^{2}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots$$
1014.2.i.d $$4$$ $$8.097$$ $$\Q(\zeta_{12})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+\zeta_{12}^{2}q^{3}+(1+\cdots)q^{4}+\cdots$$
1014.2.i.e $$4$$ $$8.097$$ $$\Q(\zeta_{12})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+\zeta_{12}^{2}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots$$
1014.2.i.f $$4$$ $$8.097$$ $$\Q(\zeta_{12})$$ None $$0$$ $$2$$ $$0$$ $$6$$ $$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+\zeta_{12}^{2}q^{3}+(1+\cdots)q^{4}+\cdots$$
1014.2.i.g $$12$$ $$8.097$$ 12.0.$$\cdots$$.1 None $$0$$ $$-6$$ $$0$$ $$0$$ $$q-\beta _{10}q^{2}-\beta _{7}q^{3}+(1-\beta _{7})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots$$
1014.2.i.h $$12$$ $$8.097$$ 12.0.$$\cdots$$.1 None $$0$$ $$6$$ $$0$$ $$0$$ $$q+\beta _{6}q^{2}+(1-\beta _{7})q^{3}+\beta _{7}q^{4}+(2\beta _{2}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1014, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1014, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(78, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(169, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(338, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(507, [\chi])$$$$^{\oplus 2}$$