# Properties

 Label 483.2.h Level $483$ Weight $2$ Character orbit 483.h Rep. character $\chi_{483}(160,\cdot)$ Character field $\Q$ Dimension $32$ Newform subspaces $3$ Sturm bound $128$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$483 = 3 \cdot 7 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 483.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$161$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$128$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(483, [\chi])$$.

Total New Old
Modular forms 68 32 36
Cusp forms 60 32 28
Eisenstein series 8 0 8

## Trace form

 $$32q - 4q^{2} + 36q^{4} - 12q^{8} - 32q^{9} + O(q^{10})$$ $$32q - 4q^{2} + 36q^{4} - 12q^{8} - 32q^{9} + 44q^{16} + 4q^{18} - 8q^{23} + 24q^{25} - 68q^{32} + 16q^{35} - 36q^{36} - 40q^{46} + 16q^{49} + 12q^{50} - 48q^{58} + 84q^{64} + 16q^{70} + 40q^{71} + 12q^{72} - 72q^{77} + 8q^{78} + 32q^{81} - 136q^{85} + 16q^{92} - 24q^{93} - 16q^{95} - 28q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(483, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
483.2.h.a $$8$$ $$3.857$$ 8.0.342102016.5 None $$-8$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}-\beta _{1}q^{3}-q^{4}+(\beta _{4}-\beta _{5})q^{5}+\cdots$$
483.2.h.b $$12$$ $$3.857$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{8}q^{2}-\beta _{5}q^{3}+(1-\beta _{7})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$$
483.2.h.c $$12$$ $$3.857$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$4$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+\beta _{9}q^{3}+(3+\beta _{7})q^{4}-\beta _{5}q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(483, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(483, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(161, [\chi])$$$$^{\oplus 2}$$