# Properties

 Label 1014.2.e Level $1014$ Weight $2$ Character orbit 1014.e Rep. character $\chi_{1014}(529,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $52$ Newform subspaces $14$ Sturm bound $364$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1014 = 2 \cdot 3 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1014.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$14$$ Sturm bound: $$364$$ Trace bound: $$5$$ 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 52 368
Cusp forms 308 52 256
Eisenstein series 112 0 112

## Trace form

 $$52 q - 2 q^{2} - 26 q^{4} - 4 q^{5} + 4 q^{8} - 26 q^{9} + O(q^{10})$$ $$52 q - 2 q^{2} - 26 q^{4} - 4 q^{5} + 4 q^{8} - 26 q^{9} - 2 q^{10} + 8 q^{11} + 8 q^{14} + 4 q^{15} - 26 q^{16} - 2 q^{17} + 4 q^{18} + 2 q^{20} - 8 q^{21} - 12 q^{22} - 8 q^{23} + 72 q^{25} - 18 q^{29} - 4 q^{30} + 16 q^{31} - 2 q^{32} + 4 q^{33} + 4 q^{34} - 26 q^{36} - 18 q^{37} + 8 q^{38} + 4 q^{40} + 2 q^{41} - 4 q^{42} - 8 q^{43} - 16 q^{44} + 2 q^{45} - 16 q^{47} - 46 q^{49} + 32 q^{51} + 20 q^{53} + 8 q^{55} - 4 q^{56} - 8 q^{57} + 6 q^{58} - 8 q^{59} - 8 q^{60} - 30 q^{61} + 4 q^{62} + 52 q^{64} + 8 q^{66} - 8 q^{67} - 2 q^{68} - 20 q^{69} + 16 q^{70} - 8 q^{71} - 2 q^{72} + 52 q^{73} + 18 q^{74} + 8 q^{75} + 56 q^{79} + 2 q^{80} - 26 q^{81} - 6 q^{82} + 4 q^{84} - 14 q^{85} + 8 q^{87} - 12 q^{88} + 20 q^{89} + 4 q^{90} + 16 q^{92} - 16 q^{94} - 8 q^{95} + 12 q^{97} + 6 q^{98} - 16 q^{99} + O(q^{100})$$

## 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.e.a $2$ $8.097$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-1$$ $$-6$$ $$2$$ $$q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1014.2.e.b $2$ $8.097$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-1$$ $$4$$ $$-2$$ $$q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1014.2.e.c $2$ $8.097$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$-4$$ $$4$$ $$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1014.2.e.d $2$ $8.097$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$2$$ $$-2$$ $$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1014.2.e.e $2$ $8.097$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$-4$$ $$2$$ $$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1014.2.e.f $2$ $8.097$ $$\Q(\sqrt{-3})$$ None $$1$$ $$1$$ $$4$$ $$-4$$ $$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1014.2.e.g $4$ $8.097$ $$\Q(\zeta_{12})$$ None $$-2$$ $$-2$$ $$8$$ $$2$$ $$q+(-1+\zeta_{12})q^{2}+(-1+\zeta_{12})q^{3}+\cdots$$
1014.2.e.h $4$ $8.097$ $$\Q(\zeta_{12})$$ None $$-2$$ $$2$$ $$0$$ $$6$$ $$q-\zeta_{12}q^{2}+\zeta_{12}q^{3}+(-1+\zeta_{12})q^{4}+\cdots$$
1014.2.e.i $4$ $8.097$ $$\Q(\zeta_{12})$$ None $$2$$ $$-2$$ $$-8$$ $$-2$$ $$q+\zeta_{12}q^{2}-\zeta_{12}q^{3}+(-1+\zeta_{12})q^{4}+\cdots$$
1014.2.e.j $4$ $8.097$ $$\Q(\zeta_{12})$$ None $$2$$ $$2$$ $$0$$ $$-6$$ $$q+\zeta_{12}q^{2}+\zeta_{12}q^{3}+(-1+\zeta_{12})q^{4}+\cdots$$
1014.2.e.k $6$ $8.097$ 6.0.64827.1 None $$-3$$ $$-3$$ $$-6$$ $$-3$$ $$q+(-1+\beta _{5})q^{2}+(-1+\beta _{5})q^{3}-\beta _{5}q^{4}+\cdots$$
1014.2.e.l $6$ $8.097$ 6.0.64827.1 None $$-3$$ $$3$$ $$2$$ $$-9$$ $$q+(-1+\beta _{5})q^{2}+(1-\beta _{5})q^{3}-\beta _{5}q^{4}+\cdots$$
1014.2.e.m $6$ $8.097$ 6.0.64827.1 None $$3$$ $$-3$$ $$6$$ $$3$$ $$q+\beta _{5}q^{2}-\beta _{5}q^{3}+(-1+\beta _{5})q^{4}+(2\beta _{2}+\cdots)q^{5}+\cdots$$
1014.2.e.n $6$ $8.097$ 6.0.64827.1 None $$3$$ $$3$$ $$-2$$ $$9$$ $$q+\beta _{5}q^{2}+\beta _{5}q^{3}+(-1+\beta _{5})q^{4}+(-2\beta _{2}+\cdots)q^{5}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(1014, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(78, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(169, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(338, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(507, [\chi])$$$$^{\oplus 2}$$