# Properties

 Label 1134.2.t Level $1134$ Weight $2$ Character orbit 1134.t Rep. character $\chi_{1134}(593,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $64$ Newform subspaces $8$ Sturm bound $432$ Trace bound $14$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1134 = 2 \cdot 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1134.t (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$63$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$8$$ Sturm bound: $$432$$ Trace bound: $$14$$ Distinguishing $$T_p$$: $$5$$, $$11$$

## 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

 $$64q + 32q^{4} - 10q^{7} + O(q^{10})$$ $$64q + 32q^{4} - 10q^{7} + 30q^{13} - 32q^{16} + 64q^{25} + 10q^{28} - 30q^{31} + 10q^{37} + 10q^{43} - 12q^{46} - 14q^{49} + 60q^{58} + 30q^{61} - 64q^{64} + 2q^{67} + 18q^{70} + 44q^{79} + 24q^{85} - 12q^{91} + 30q^{97} + O(q^{100})$$

## 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.t.a $$4$$ $$9.055$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$-10$$ $$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{4}+\cdots$$
1134.2.t.b $$4$$ $$9.055$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{4}+\cdots$$
1134.2.t.c $$4$$ $$9.055$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{4}+\cdots$$
1134.2.t.d $$4$$ $$9.055$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{4}+\cdots$$
1134.2.t.e $$8$$ $$9.055$$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+(\zeta_{24}-\zeta_{24}^{3})q^{2}+(1-\zeta_{24}^{2})q^{4}+\cdots$$
1134.2.t.f $$8$$ $$9.055$$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+(-\zeta_{24}+\zeta_{24}^{3})q^{2}+(1-\zeta_{24}^{2})q^{4}+\cdots$$
1134.2.t.g $$16$$ $$9.055$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\beta _{9}q^{2}+(1+\beta _{2})q^{4}+\beta _{6}q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots$$
1134.2.t.h $$16$$ $$9.055$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\beta _{4}q^{2}-\beta _{2}q^{4}-\beta _{6}q^{5}+(\beta _{3}+\beta _{6}+\cdots)q^{7}+\cdots$$

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

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