# Properties

 Label 700.2.t Level $700$ Weight $2$ Character orbit 700.t Rep. character $\chi_{700}(199,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $136$ Newform subspaces $5$ Sturm bound $240$ Trace bound $12$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$700 = 2^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 700.t (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$140$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$5$$ Sturm bound: $$240$$ Trace bound: $$12$$ Distinguishing $$T_p$$: $$3$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(700, [\chi])$$.

Total New Old
Modular forms 264 152 112
Cusp forms 216 136 80
Eisenstein series 48 16 32

## Trace form

 $$136q + 2q^{4} + 64q^{9} + O(q^{10})$$ $$136q + 2q^{4} + 64q^{9} + 18q^{14} - 10q^{16} + 12q^{21} - 12q^{24} + 6q^{26} + 32q^{29} + 60q^{36} + 4q^{44} + 4q^{46} - 102q^{54} - 38q^{56} - 12q^{61} - 88q^{64} - 96q^{66} - 62q^{74} - 108q^{81} - 94q^{84} + 56q^{86} + 132q^{89} - 66q^{94} + 18q^{96} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(700, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
700.2.t.a $$4$$ $$5.590$$ $$\Q(\zeta_{12})$$ None $$-2$$ $$-6$$ $$0$$ $$-8$$ $$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-1+\cdots)q^{3}+\cdots$$
700.2.t.b $$4$$ $$5.590$$ $$\Q(\zeta_{12})$$ None $$2$$ $$6$$ $$0$$ $$8$$ $$q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(1+\zeta_{12}^{2}+\cdots)q^{3}+\cdots$$
700.2.t.c $$32$$ $$5.590$$ None $$0$$ $$0$$ $$0$$ $$0$$
700.2.t.d $$32$$ $$5.590$$ None $$0$$ $$0$$ $$0$$ $$0$$
700.2.t.e $$64$$ $$5.590$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(700, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(700, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 2}$$