Properties

 Label 4032.2.h Level 4032 Weight 2 Character orbit h Rep. character $$\chi_{4032}(575,\cdot)$$ Character field $$\Q$$ Dimension 48 Newform subspaces 8 Sturm bound 1536 Trace bound 25

Related objects

Defining parameters

 Level: $$N$$ = $$4032 = 2^{6} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 4032.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$12$$ Character field: $$\Q$$ Newform subspaces: $$8$$ Sturm bound: $$1536$$ Trace bound: $$25$$ Distinguishing $$T_p$$: $$5$$, $$11$$, $$13$$

Dimensions

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

Total New Old
Modular forms 816 48 768
Cusp forms 720 48 672
Eisenstein series 96 0 96

Trace form

 $$48q + O(q^{10})$$ $$48q - 48q^{25} - 48q^{49} - 64q^{61} + 64q^{85} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(4032, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
4032.2.h.a $$4$$ $$32.196$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-2\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}-\zeta_{8}^{3}q^{11}-6q^{13}+\cdots$$
4032.2.h.b $$4$$ $$32.196$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}+2\zeta_{8}^{3}q^{11}+5\zeta_{8}^{2}q^{17}+\cdots$$
4032.2.h.c $$4$$ $$32.196$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-2\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}+\zeta_{8}^{3}q^{11}+2q^{13}+\cdots$$
4032.2.h.d $$4$$ $$32.196$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}q^{7}+3\zeta_{8}^{3}q^{11}+2q^{13}+2\zeta_{8}^{2}q^{17}+\cdots$$
4032.2.h.e $$4$$ $$32.196$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}+4\zeta_{8}^{3}q^{11}+4q^{13}+\cdots$$
4032.2.h.f $$8$$ $$32.196$$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{24}^{2}+\zeta_{24}^{7})q^{5}+\zeta_{24}q^{7}+(\zeta_{24}^{3}+\cdots)q^{11}+\cdots$$
4032.2.h.g $$8$$ $$32.196$$ 8.0.5473632256.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{5}+\beta _{6})q^{5}-\beta _{1}q^{7}+(-\beta _{4}-2\beta _{7})q^{11}+\cdots$$
4032.2.h.h $$12$$ $$32.196$$ 12.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{5}+\beta _{3}q^{7}+(-\beta _{5}-\beta _{6})q^{11}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(4032, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(252, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(288, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(336, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(576, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(672, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1008, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1344, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(2016, [\chi])$$$$^{\oplus 2}$$