Properties

 Label 345.2.i Level $345$ Weight $2$ Character orbit 345.i Rep. character $\chi_{345}(47,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $88$ Newform subspaces $3$ Sturm bound $96$ Trace bound $2$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$345 = 3 \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 345.i (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q(i)$$ Newform subspaces: $$3$$ Sturm bound: $$96$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(345, [\chi])$$.

Total New Old
Modular forms 104 88 16
Cusp forms 88 88 0
Eisenstein series 16 0 16

Trace form

 $$88q - 8q^{7} + O(q^{10})$$ $$88q - 8q^{7} - 8q^{10} - 16q^{13} + 12q^{15} - 88q^{16} - 28q^{18} + 8q^{21} + 24q^{22} + 12q^{27} - 24q^{28} + 16q^{30} - 16q^{31} + 4q^{33} - 48q^{37} + 64q^{40} - 32q^{42} - 32q^{43} - 24q^{45} + 28q^{48} - 24q^{51} + 32q^{52} - 24q^{55} - 40q^{57} + 8q^{58} + 20q^{60} + 16q^{61} + 68q^{63} + 72q^{66} + 16q^{67} - 104q^{70} + 36q^{72} + 24q^{73} - 36q^{75} + 16q^{76} - 100q^{78} - 8q^{81} + 16q^{82} + 32q^{85} - 40q^{87} + 120q^{88} - 4q^{90} - 96q^{91} - 56q^{93} - 80q^{96} - 8q^{97} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(345, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
345.2.i.a $$4$$ $$2.755$$ $$\Q(\zeta_{8})$$ None $$-4$$ $$-4$$ $$0$$ $$-8$$ $$q+(-1+\zeta_{8}^{2})q^{2}+(-1+\zeta_{8}+\zeta_{8}^{3})q^{3}+\cdots$$
345.2.i.b $$4$$ $$2.755$$ $$\Q(\zeta_{8})$$ None $$4$$ $$0$$ $$0$$ $$-8$$ $$q+(1+\zeta_{8}^{2})q^{2}+(-\zeta_{8}-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots$$
345.2.i.c $$80$$ $$2.755$$ None $$0$$ $$4$$ $$0$$ $$8$$