Properties

 Label 3330.2.e Level $3330$ Weight $2$ Character orbit 3330.e Rep. character $\chi_{3330}(739,\cdot)$ Character field $\Q$ Dimension $96$ Newform subspaces $8$ Sturm bound $1368$ Trace bound $2$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3330.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$185$$ Character field: $$\Q$$ Newform subspaces: $$8$$ Sturm bound: $$1368$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$7$$, $$13$$, $$17$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(3330, [\chi])$$.

Total New Old
Modular forms 700 96 604
Cusp forms 668 96 572
Eisenstein series 32 0 32

Trace form

 $$96q + 96q^{4} + O(q^{10})$$ $$96q + 96q^{4} + 2q^{10} + 8q^{11} + 96q^{16} + 22q^{25} - 20q^{26} - 12q^{34} + 2q^{40} - 8q^{41} + 8q^{44} + 28q^{46} - 92q^{49} + 96q^{64} + 4q^{65} - 16q^{70} + 40q^{71} - 16q^{85} - 20q^{86} + 44q^{95} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(3330, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
3330.2.e.a $$2$$ $$26.590$$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$0$$ $$4$$ $$0$$ $$q-q^{2}+q^{4}+(2-i)q^{5}+3iq^{7}-q^{8}+\cdots$$
3330.2.e.b $$2$$ $$26.590$$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$-4$$ $$0$$ $$q+q^{2}+q^{4}+(-2+i)q^{5}+3iq^{7}+\cdots$$
3330.2.e.c $$10$$ $$26.590$$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$-10$$ $$0$$ $$-3$$ $$0$$ $$q-q^{2}+q^{4}+\beta _{5}q^{5}-\beta _{2}q^{7}-q^{8}+\cdots$$
3330.2.e.d $$10$$ $$26.590$$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$10$$ $$0$$ $$3$$ $$0$$ $$q+q^{2}+q^{4}-\beta _{5}q^{5}-\beta _{2}q^{7}+q^{8}+\cdots$$
3330.2.e.e $$16$$ $$26.590$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$-16$$ $$0$$ $$-2$$ $$0$$ $$q-q^{2}+q^{4}-\beta _{11}q^{5}-\beta _{14}q^{7}-q^{8}+\cdots$$
3330.2.e.f $$16$$ $$26.590$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$16$$ $$0$$ $$2$$ $$0$$ $$q+q^{2}+q^{4}+\beta _{11}q^{5}-\beta _{14}q^{7}+q^{8}+\cdots$$
3330.2.e.g $$20$$ $$26.590$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$-20$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+q^{4}+\beta _{10}q^{5}-\beta _{11}q^{7}-q^{8}+\cdots$$
3330.2.e.h $$20$$ $$26.590$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$20$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+q^{4}-\beta _{10}q^{5}-\beta _{11}q^{7}+q^{8}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(3330, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(3330, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(185, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(370, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(555, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1110, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1665, [\chi])$$$$^{\oplus 2}$$