Properties

 Label 735.2.j Level $735$ Weight $2$ Character orbit 735.j Rep. character $\chi_{735}(197,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $144$ Newform subspaces $8$ Sturm bound $224$ Trace bound $3$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$735 = 3 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 735.j (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q(i)$$ Newform subspaces: $$8$$ Sturm bound: $$224$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$, $$13$$, $$17$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(735, [\chi])$$.

Total New Old
Modular forms 256 184 72
Cusp forms 192 144 48
Eisenstein series 64 40 24

Trace form

 $$144q + 4q^{3} + O(q^{10})$$ $$144q + 4q^{3} + 16q^{10} - 16q^{12} + 8q^{13} + 4q^{15} - 80q^{16} + 4q^{18} - 40q^{22} + 24q^{25} + 16q^{27} - 28q^{33} - 56q^{36} + 24q^{37} - 64q^{40} + 16q^{43} - 20q^{45} + 64q^{46} - 16q^{48} + 32q^{51} - 40q^{55} + 8q^{57} - 16q^{58} - 76q^{60} - 32q^{61} + 16q^{66} - 24q^{67} + 52q^{72} - 32q^{73} + 60q^{75} - 32q^{76} - 152q^{78} - 56q^{81} + 80q^{82} - 56q^{85} - 4q^{87} - 192q^{88} + 24q^{90} + 24q^{93} + 96q^{96} - 24q^{97} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(735, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
735.2.j.a $$8$$ $$5.869$$ $$\Q(\zeta_{24})$$ None $$0$$ $$-4$$ $$8$$ $$0$$ $$q+(2\zeta_{24}-2\zeta_{24}^{5})q^{2}+(\zeta_{24}+\zeta_{24}^{2}+\cdots)q^{3}+\cdots$$
735.2.j.b $$8$$ $$5.869$$ $$\Q(\zeta_{24})$$ None $$0$$ $$4$$ $$-8$$ $$0$$ $$q+2\zeta_{24}^{3}q^{2}+(\zeta_{24}^{2}+\zeta_{24}^{4}-\zeta_{24}^{6}+\cdots)q^{3}+\cdots$$
735.2.j.c $$16$$ $$5.869$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$-4$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}+(\beta _{1}-\beta _{2}-\beta _{8})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots$$
735.2.j.d $$16$$ $$5.869$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$4$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}+(-\beta _{6}+\beta _{7}+\beta _{15})q^{3}+(\beta _{3}+\cdots)q^{4}+\cdots$$
735.2.j.e $$24$$ $$5.869$$ None $$0$$ $$-2$$ $$0$$ $$0$$
735.2.j.f $$24$$ $$5.869$$ None $$0$$ $$0$$ $$0$$ $$0$$
735.2.j.g $$24$$ $$5.869$$ None $$0$$ $$2$$ $$0$$ $$0$$
735.2.j.h $$24$$ $$5.869$$ None $$0$$ $$4$$ $$0$$ $$0$$

Decomposition of $$S_{2}^{\mathrm{old}}(735, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(735, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 2}$$