# Properties

 Label 3072.2.d Level $3072$ Weight $2$ Character orbit 3072.d Rep. character $\chi_{3072}(1537,\cdot)$ Character field $\Q$ Dimension $64$ Newform subspaces $10$ Sturm bound $1024$ Trace bound $17$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3072 = 2^{10} \cdot 3$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3072.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$10$$ Sturm bound: $$1024$$ Trace bound: $$17$$ Distinguishing $$T_p$$: $$5$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(3072, [\chi])$$.

Total New Old
Modular forms 560 64 496
Cusp forms 464 64 400
Eisenstein series 96 0 96

## Trace form

 $$64q - 64q^{9} + O(q^{10})$$ $$64q - 64q^{9} - 64q^{25} + 64q^{49} + 64q^{81} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(3072, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
3072.2.d.a $$4$$ $$24.530$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}q^{3}-\zeta_{8}^{3}q^{7}-q^{9}-\zeta_{8}^{2}q^{13}+\cdots$$
3072.2.d.b $$4$$ $$24.530$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}q^{3}-\zeta_{8}^{2}q^{5}-q^{9}+4\zeta_{8}q^{11}+\cdots$$
3072.2.d.c $$4$$ $$24.530$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}+2\zeta_{8}^{3}q^{7}-q^{9}+\cdots$$
3072.2.d.d $$4$$ $$24.530$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}q^{3}+2\zeta_{8}^{2}q^{5}+3\zeta_{8}^{3}q^{7}-q^{9}+\cdots$$
3072.2.d.e $$8$$ $$24.530$$ $$\Q(\zeta_{16})$$ None $$0$$ $$0$$ $$0$$ $$-16$$ $$q+\zeta_{16}q^{3}+(\zeta_{16}^{2}-\zeta_{16}^{3})q^{5}+(-2+\cdots)q^{7}+\cdots$$
3072.2.d.f $$8$$ $$24.530$$ 8.0.18939904.2 None $$0$$ $$0$$ $$0$$ $$-8$$ $$q-\beta _{4}q^{3}+(\beta _{4}+\beta _{6})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$$
3072.2.d.g $$8$$ $$24.530$$ 8.0.40960000.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{6}q^{5}+(\beta _{2}-\beta _{7})q^{7}-q^{9}+\cdots$$
3072.2.d.h $$8$$ $$24.530$$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{24}q^{3}+(-\zeta_{24}^{2}-\zeta_{24}^{7})q^{5}+\zeta_{24}^{3}q^{7}+\cdots$$
3072.2.d.i $$8$$ $$24.530$$ 8.0.18939904.2 None $$0$$ $$0$$ $$0$$ $$8$$ $$q+\beta _{4}q^{3}+(\beta _{4}+\beta _{6})q^{5}+(1-\beta _{1})q^{7}+\cdots$$
3072.2.d.j $$8$$ $$24.530$$ $$\Q(\zeta_{16})$$ None $$0$$ $$0$$ $$0$$ $$16$$ $$q-\zeta_{16}q^{3}+(\zeta_{16}^{2}-\zeta_{16}^{3})q^{5}+(2-\zeta_{16}^{5}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(3072, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(3072, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(128, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(256, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(384, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(512, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(768, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1024, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1536, [\chi])$$$$^{\oplus 2}$$