# Properties

 Label 2352.2.h Level $2352$ Weight $2$ Character orbit 2352.h Rep. character $\chi_{2352}(2255,\cdot)$ Character field $\Q$ Dimension $82$ Newform subspaces $16$ Sturm bound $896$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2352 = 2^{4} \cdot 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2352.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$12$$ Character field: $$\Q$$ Newform subspaces: $$16$$ Sturm bound: $$896$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$5$$, $$11$$, $$13$$, $$47$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2352, [\chi])$$.

Total New Old
Modular forms 496 82 414
Cusp forms 400 82 318
Eisenstein series 96 0 96

## Trace form

 $$82q - 6q^{9} + O(q^{10})$$ $$82q - 6q^{9} + 4q^{13} - 94q^{25} - 28q^{37} + 24q^{45} + 36q^{57} + 20q^{61} - 24q^{69} + 52q^{73} - 6q^{81} + 48q^{85} + 12q^{93} - 44q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2352, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2352.2.h.a $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{6}q^{3}-3q^{9}-7q^{13}+3\zeta_{6}q^{19}+\cdots$$
2352.2.h.b $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{6}q^{3}-3q^{9}-5q^{13}+5\zeta_{6}q^{19}+\cdots$$
2352.2.h.c $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{6}q^{3}-3q^{9}+2q^{13}+2\zeta_{6}q^{19}+\cdots$$
2352.2.h.d $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{6}q^{3}-3q^{9}+5q^{13}-5\zeta_{6}q^{19}+\cdots$$
2352.2.h.e $$2$$ $$18.781$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{6}q^{3}-3q^{9}+7q^{13}-3\zeta_{6}q^{19}+\cdots$$
2352.2.h.f $$4$$ $$18.781$$ $$\Q(\zeta_{8})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+(-1+\zeta_{8}^{2})q^{3}-\zeta_{8}q^{5}+(-1-2\zeta_{8}^{2}+\cdots)q^{9}+\cdots$$
2352.2.h.g $$4$$ $$18.781$$ $$\Q(\sqrt{-3}, \sqrt{-14})$$ $$\Q(\sqrt{-21})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+\beta _{1}q^{5}-3q^{9}-\beta _{3}q^{11}+\cdots$$
2352.2.h.h $$4$$ $$18.781$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}+(1-2\zeta_{8}^{2}+\cdots)q^{9}+\cdots$$
2352.2.h.i $$4$$ $$18.781$$ $$\Q(i, \sqrt{11})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}+\beta _{2})q^{3}+(-1-2\beta _{3})q^{5}+\cdots$$
2352.2.h.j $$4$$ $$18.781$$ $$\Q(i, \sqrt{11})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+(-1-2\beta _{3})q^{5}+(3+\beta _{3})q^{9}+\cdots$$
2352.2.h.k $$4$$ $$18.781$$ $$\Q(\zeta_{8})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q+(1-\zeta_{8}^{2})q^{3}-\zeta_{8}q^{5}+(-1-2\zeta_{8}^{2}+\cdots)q^{9}+\cdots$$
2352.2.h.l $$8$$ $$18.781$$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}^{2}q^{3}+\zeta_{24}^{4}q^{5}-\zeta_{24}^{5}q^{9}+\cdots$$
2352.2.h.m $$8$$ $$18.781$$ 8.0.8275904784.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{5}q^{3}-\beta _{7}q^{5}+(-\beta _{4}-\beta _{7})q^{9}+\cdots$$
2352.2.h.n $$8$$ $$18.781$$ 8.0.8275904784.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{3}-\beta _{7}q^{5}+(-\beta _{2}+\beta _{7})q^{9}+\cdots$$
2352.2.h.o $$8$$ $$18.781$$ 8.0.56070144.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+\beta _{2}q^{5}+(1-\beta _{5}+\beta _{7})q^{9}+\cdots$$
2352.2.h.p $$16$$ $$18.781$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{9}q^{3}+\beta _{13}q^{5}-\beta _{3}q^{9}-\beta _{7}q^{13}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2352, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2352, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(336, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(588, [\chi])$$$$^{\oplus 3}$$