# Properties

 Label 345.2.b Level $345$ Weight $2$ Character orbit 345.b Rep. character $\chi_{345}(139,\cdot)$ Character field $\Q$ Dimension $24$ Newform subspaces $4$ Sturm bound $96$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$345 = 3 \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 345.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$96$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$2$$, $$7$$

## Dimensions

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

Total New Old
Modular forms 52 24 28
Cusp forms 44 24 20
Eisenstein series 8 0 8

## Trace form

 $$24q - 28q^{4} + 4q^{5} + 4q^{6} - 24q^{9} + O(q^{10})$$ $$24q - 28q^{4} + 4q^{5} + 4q^{6} - 24q^{9} - 8q^{14} - 4q^{15} + 36q^{16} + 8q^{19} + 4q^{20} - 8q^{21} - 12q^{24} - 32q^{26} + 12q^{29} - 8q^{30} + 20q^{31} + 32q^{34} - 36q^{35} + 28q^{36} - 8q^{39} + 24q^{40} + 28q^{41} - 40q^{44} - 4q^{45} + 8q^{46} - 52q^{49} + 48q^{50} - 4q^{54} + 12q^{59} + 36q^{60} - 100q^{64} + 16q^{65} - 8q^{66} - 8q^{69} + 64q^{70} - 4q^{71} - 88q^{74} + 8q^{75} - 32q^{76} + 40q^{79} + 76q^{80} + 24q^{81} + 56q^{84} + 12q^{85} - 48q^{86} - 48q^{89} - 48q^{91} - 80q^{94} + 8q^{95} + 28q^{96} + O(q^{100})$$

## 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.b.a $$2$$ $$2.755$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{2}+iq^{3}+q^{4}+(1+2i)q^{5}-q^{6}+\cdots$$
345.2.b.b $$2$$ $$2.755$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+iq^{2}-iq^{3}+q^{4}+(2-i)q^{5}+q^{6}+\cdots$$
345.2.b.c $$6$$ $$2.755$$ 6.0.350464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{2}-\beta _{3}q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$$
345.2.b.d $$14$$ $$2.755$$ $$\mathbb{Q}[x]/(x^{14} + \cdots)$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\beta _{5}q^{2}-\beta _{2}q^{3}+(-2-\beta _{8}+\beta _{9}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(345, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(345, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(115, [\chi])$$$$^{\oplus 2}$$