Properties

 Label 96.3.h Level $96$ Weight $3$ Character orbit 96.h Rep. character $\chi_{96}(17,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $3$ Sturm bound $48$ Trace bound $3$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$96 = 2^{5} \cdot 3$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 96.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$24$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$48$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$5$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(96, [\chi])$$.

Total New Old
Modular forms 40 10 30
Cusp forms 24 6 18
Eisenstein series 16 4 12

Trace form

 $$6q + 4q^{7} - 2q^{9} + O(q^{10})$$ $$6q + 4q^{7} - 2q^{9} + 20q^{15} - 14q^{25} - 60q^{31} - 12q^{33} - 112q^{39} - 30q^{49} + 232q^{55} + 56q^{57} + 260q^{63} + 76q^{73} - 380q^{79} + 38q^{81} - 396q^{87} + 92q^{97} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(96, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
96.3.h.a $$1$$ $$2.616$$ $$\Q$$ $$\Q(\sqrt{-6})$$ $$0$$ $$-3$$ $$2$$ $$10$$ $$q-3q^{3}+2q^{5}+10q^{7}+9q^{9}+10q^{11}+\cdots$$
96.3.h.b $$1$$ $$2.616$$ $$\Q$$ $$\Q(\sqrt{-6})$$ $$0$$ $$3$$ $$-2$$ $$10$$ $$q+3q^{3}-2q^{5}+10q^{7}+9q^{9}-10q^{11}+\cdots$$
96.3.h.c $$4$$ $$2.616$$ $$\Q(\sqrt{2}, \sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$-16$$ $$q+(-\beta _{1}-\beta _{2})q^{3}-2\beta _{1}q^{5}-4q^{7}+\cdots$$

Decomposition of $$S_{3}^{\mathrm{old}}(96, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(96, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 3}$$