# Properties

 Label 1134.2.e Level $1134$ Weight $2$ Character orbit 1134.e Rep. character $\chi_{1134}(865,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $64$ Newform subspaces $22$ Sturm bound $432$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1134 = 2 \cdot 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1134.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$63$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$22$$ Sturm bound: $$432$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$, $$11$$, $$17$$, $$23$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1134, [\chi])$$.

Total New Old
Modular forms 480 64 416
Cusp forms 384 64 320
Eisenstein series 96 0 96

## Trace form

 $$64 q + 64 q^{4} + 10 q^{7} + O(q^{10})$$ $$64 q + 64 q^{4} + 10 q^{7} - 10 q^{13} + 64 q^{16} + 20 q^{19} - 32 q^{25} + 10 q^{28} + 20 q^{31} - 10 q^{37} - 10 q^{43} + 12 q^{46} - 2 q^{49} - 10 q^{52} + 60 q^{55} - 30 q^{58} - 28 q^{61} + 64 q^{64} - 4 q^{67} + 54 q^{70} - 4 q^{73} + 20 q^{76} + 128 q^{79} - 24 q^{85} + 8 q^{91} + 48 q^{94} - 10 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1134, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1134.2.e.a $2$ $9.055$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$-3$$ $$-1$$ $$q-q^{2}+q^{4}+(-3+3\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots$$
1134.2.e.b $2$ $9.055$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$-2$$ $$4$$ $$q-q^{2}+q^{4}+(-2+2\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+\cdots$$
1134.2.e.c $2$ $9.055$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$0$$ $$-1$$ $$q-q^{2}+q^{4}+(1-3\zeta_{6})q^{7}-q^{8}-6\zeta_{6}q^{11}+\cdots$$
1134.2.e.d $2$ $9.055$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$0$$ $$5$$ $$q-q^{2}+q^{4}+(2+\zeta_{6})q^{7}-q^{8}+4\zeta_{6}q^{13}+\cdots$$
1134.2.e.e $2$ $9.055$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$1$$ $$-5$$ $$q-q^{2}+q^{4}+(1-\zeta_{6})q^{5}+(-2-\zeta_{6})q^{7}+\cdots$$
1134.2.e.f $2$ $9.055$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$3$$ $$-1$$ $$q-q^{2}+q^{4}+(3-3\zeta_{6})q^{5}+(1-3\zeta_{6})q^{7}+\cdots$$
1134.2.e.g $2$ $9.055$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$3$$ $$5$$ $$q-q^{2}+q^{4}+(3-3\zeta_{6})q^{5}+(2+\zeta_{6})q^{7}+\cdots$$
1134.2.e.h $2$ $9.055$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$4$$ $$-5$$ $$q-q^{2}+q^{4}+(4-4\zeta_{6})q^{5}+(-2-\zeta_{6})q^{7}+\cdots$$
1134.2.e.i $2$ $9.055$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$-4$$ $$-5$$ $$q+q^{2}+q^{4}+(-4+4\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots$$
1134.2.e.j $2$ $9.055$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$-3$$ $$-1$$ $$q+q^{2}+q^{4}+(-3+3\zeta_{6})q^{5}+(1-3\zeta_{6})q^{7}+\cdots$$
1134.2.e.k $2$ $9.055$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$-3$$ $$5$$ $$q+q^{2}+q^{4}+(-3+3\zeta_{6})q^{5}+(2+\zeta_{6})q^{7}+\cdots$$
1134.2.e.l $2$ $9.055$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$-1$$ $$-5$$ $$q+q^{2}+q^{4}+(-1+\zeta_{6})q^{5}+(-2-\zeta_{6})q^{7}+\cdots$$
1134.2.e.m $2$ $9.055$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$0$$ $$-1$$ $$q+q^{2}+q^{4}+(1-3\zeta_{6})q^{7}+q^{8}+6\zeta_{6}q^{11}+\cdots$$
1134.2.e.n $2$ $9.055$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$0$$ $$5$$ $$q+q^{2}+q^{4}+(2+\zeta_{6})q^{7}+q^{8}+4\zeta_{6}q^{13}+\cdots$$
1134.2.e.o $2$ $9.055$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$2$$ $$4$$ $$q+q^{2}+q^{4}+(2-2\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+\cdots$$
1134.2.e.p $2$ $9.055$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$3$$ $$-1$$ $$q+q^{2}+q^{4}+(3-3\zeta_{6})q^{5}+(-2+3\zeta_{6})q^{7}+\cdots$$
1134.2.e.q $4$ $9.055$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None $$-4$$ $$0$$ $$-2$$ $$0$$ $$q-q^{2}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}-\beta _{1}q^{7}+\cdots$$
1134.2.e.r $4$ $9.055$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$-4$$ $$0$$ $$0$$ $$-2$$ $$q-q^{2}+q^{4}+(-1-\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots$$
1134.2.e.s $4$ $9.055$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$4$$ $$0$$ $$0$$ $$-2$$ $$q+q^{2}+q^{4}+(-1-\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots$$
1134.2.e.t $4$ $9.055$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None $$4$$ $$0$$ $$2$$ $$0$$ $$q+q^{2}+q^{4}+(1+\beta _{1}+\beta _{2})q^{5}+\beta _{1}q^{7}+\cdots$$
1134.2.e.u $8$ $9.055$ 8.0.454201344.7 None $$-8$$ $$0$$ $$-4$$ $$6$$ $$q-q^{2}+q^{4}+(-\beta _{3}+\beta _{4}-\beta _{5})q^{5}+\cdots$$
1134.2.e.v $8$ $9.055$ 8.0.454201344.7 None $$8$$ $$0$$ $$4$$ $$6$$ $$q+q^{2}+q^{4}+(\beta _{3}-\beta _{4}+\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1134, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1134, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(189, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(378, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(567, [\chi])$$$$^{\oplus 2}$$