# Properties

 Label 230.2.e Level $230$ Weight $2$ Character orbit 230.e Rep. character $\chi_{230}(137,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $24$ Newform subspaces $3$ Sturm bound $72$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$230 = 2 \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 230.e (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$115$$ Character field: $$\Q(i)$$ Newform subspaces: $$3$$ Sturm bound: $$72$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$3$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(230, [\chi])$$.

Total New Old
Modular forms 80 24 56
Cusp forms 64 24 40
Eisenstein series 16 0 16

## Trace form

 $$24q + 8q^{3} + 8q^{6} + O(q^{10})$$ $$24q + 8q^{3} + 8q^{6} + 8q^{12} - 16q^{13} - 24q^{16} - 16q^{18} - 8q^{23} + 8q^{26} - 16q^{27} - 24q^{31} + 8q^{35} + 32q^{36} + 24q^{41} + 8q^{46} - 8q^{47} - 8q^{48} - 8q^{50} - 16q^{52} + 32q^{62} - 24q^{70} - 104q^{71} - 16q^{72} + 88q^{73} - 8q^{75} + 24q^{77} - 40q^{78} - 40q^{81} - 40q^{82} + 56q^{85} - 40q^{87} - 8q^{92} - 56q^{93} - 96q^{95} - 8q^{96} + 64q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(230, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
230.2.e.a $$8$$ $$1.837$$ 8.0.110166016.2 None $$0$$ $$-4$$ $$-4$$ $$0$$ $$q-\beta _{3}q^{2}+(-1-\beta _{2}-\beta _{6}-\beta _{7})q^{3}+\cdots$$
230.2.e.b $$8$$ $$1.837$$ 8.0.110166016.2 None $$0$$ $$-4$$ $$4$$ $$0$$ $$q-\beta _{3}q^{2}+(-1-\beta _{2}-\beta _{6}-\beta _{7})q^{3}+\cdots$$
230.2.e.c $$8$$ $$1.837$$ $$\Q(\zeta_{16})$$ None $$0$$ $$16$$ $$0$$ $$0$$ $$q+\zeta_{16}^{6}q^{2}+(2+2\zeta_{16}^{4})q^{3}-\zeta_{16}^{4}q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(230, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(230, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(115, [\chi])$$$$^{\oplus 2}$$