# Properties

 Label 700.2.r Level $700$ Weight $2$ Character orbit 700.r Rep. character $\chi_{700}(149,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $24$ Newform subspaces $4$ Sturm bound $240$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$700 = 2^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 700.r (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ Sturm bound: $$240$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$3$$, $$11$$

## Dimensions

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

Total New Old
Modular forms 276 24 252
Cusp forms 204 24 180
Eisenstein series 72 0 72

## Trace form

 $$24q + 20q^{9} + O(q^{10})$$ $$24q + 20q^{9} - 10q^{11} + 10q^{19} + 4q^{21} + 12q^{31} + 16q^{39} + 76q^{41} - 24q^{49} + 24q^{51} - 8q^{59} - 44q^{61} - 36q^{69} - 44q^{71} - 28q^{79} - 68q^{81} + 22q^{89} + 26q^{91} - 12q^{99} + O(q^{100})$$

## 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.r.a $$4$$ $$5.590$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{3}+(\zeta_{12}+2\zeta_{12}^{3})q^{7}-2\zeta_{12}^{2}q^{9}+\cdots$$
700.2.r.b $$4$$ $$5.590$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{3}+(-2\zeta_{12}-\zeta_{12}^{3})q^{7}-2\zeta_{12}^{2}q^{9}+\cdots$$
700.2.r.c $$4$$ $$5.590$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3\zeta_{12}q^{3}+(3\zeta_{12}-2\zeta_{12}^{3})q^{7}+6\zeta_{12}^{2}q^{9}+\cdots$$
700.2.r.d $$12$$ $$5.590$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{6}+\beta _{11})q^{3}+(\beta _{4}-\beta _{10})q^{7}+(-2\beta _{1}+\cdots)q^{9}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(700, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(350, [\chi])$$$$^{\oplus 2}$$