# Properties

 Label 4032.2.i Level 4032 Weight 2 Character orbit i Rep. character $$\chi_{4032}(1889,\cdot)$$ Character field $$\Q$$ Dimension 64 Newforms 3 Sturm bound 1536 Trace bound 47

# Related objects

## Defining parameters

 Level: $$N$$ = $$4032 = 2^{6} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 4032.i (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$168$$ Character field: $$\Q$$ Newforms: $$3$$ Sturm bound: $$1536$$ Trace bound: $$47$$ Distinguishing $$T_p$$: $$5$$, $$47$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(4032, [\chi])$$.

Total New Old
Modular forms 816 64 752
Cusp forms 720 64 656
Eisenstein series 96 0 96

## Trace form

 $$64q$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$64q$$ $$\mathstrut -\mathstrut 64q^{25}$$ $$\mathstrut +\mathstrut 32q^{49}$$ $$\mathstrut +\mathstrut O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(4032, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
4032.2.i.a $$8$$ $$32.196$$ 8.0.40960000.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{5}+(-\beta _{2}+\beta _{4})q^{7}+\beta _{3}q^{11}+\cdots$$
4032.2.i.b $$8$$ $$32.196$$ 8.0.40960000.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{5}+(-\beta _{2}-\beta _{4})q^{7}-\beta _{3}q^{11}+\cdots$$
4032.2.i.c $$48$$ $$32.196$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(4032, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(4032, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(168, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(504, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(672, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1344, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(2016, [\chi])$$$$^{\oplus 2}$$