# Properties

 Label 384.3.i Level $384$ Weight $3$ Character orbit 384.i Rep. character $\chi_{384}(161,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $56$ Newform subspaces $4$ Sturm bound $192$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$384 = 2^{7} \cdot 3$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 384.i (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$48$$ Character field: $$\Q(i)$$ Newform subspaces: $$4$$ Sturm bound: $$192$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$5$$, $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(384, [\chi])$$.

Total New Old
Modular forms 288 72 216
Cusp forms 224 56 168
Eisenstein series 64 16 48

## Trace form

 $$56q + O(q^{10})$$ $$56q + 8q^{13} - 32q^{21} - 8q^{33} + 8q^{37} + 104q^{45} - 72q^{49} + 72q^{61} + 40q^{69} - 8q^{81} + 128q^{85} + 136q^{93} - 16q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(384, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
384.3.i.a $$8$$ $$10.463$$ 8.0.629407744.1 None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+(\beta _{1}-\beta _{2}-\beta _{3})q^{3}+(3\beta _{4}-\beta _{6}-\beta _{7})q^{5}+\cdots$$
384.3.i.b $$8$$ $$10.463$$ 8.0.629407744.1 None $$0$$ $$4$$ $$0$$ $$0$$ $$q+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(3\beta _{4}-\beta _{6}+\cdots)q^{5}+\cdots$$
384.3.i.c $$20$$ $$10.463$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$-6$$ $$0$$ $$0$$ $$q-\beta _{5}q^{3}+(\beta _{8}-\beta _{9}-\beta _{10})q^{5}-\beta _{6}q^{7}+\cdots$$
384.3.i.d $$20$$ $$10.463$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$6$$ $$0$$ $$0$$ $$q+\beta _{5}q^{3}+(\beta _{8}-\beta _{9}-\beta _{10})q^{5}+\beta _{6}q^{7}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(384, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(384, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 2}$$