# Properties

 Label 345.2.s Level $345$ Weight $2$ Character orbit 345.s Rep. character $\chi_{345}(11,\cdot)$ Character field $\Q(\zeta_{22})$ Dimension $320$ Newform subspaces $2$ 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.s (of order $$22$$ and degree $$10$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$69$$ Character field: $$\Q(\zeta_{22})$$ Newform subspaces: $$2$$ Sturm bound: $$96$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

Total New Old
Modular forms 520 320 200
Cusp forms 440 320 120
Eisenstein series 80 0 80

## Trace form

 $$320q + 28q^{4} - 2q^{6} + 4q^{9} + O(q^{10})$$ $$320q + 28q^{4} - 2q^{6} + 4q^{9} - 6q^{12} + 4q^{16} + 22q^{18} - 66q^{21} - 132q^{24} - 32q^{25} - 54q^{27} + 16q^{31} - 22q^{34} - 58q^{36} - 8q^{39} - 154q^{40} - 88q^{43} - 164q^{46} + 46q^{48} - 68q^{49} + 4q^{52} - 30q^{54} - 28q^{55} + 66q^{57} - 4q^{58} + 44q^{61} + 110q^{63} - 16q^{64} + 88q^{66} + 44q^{67} + 20q^{69} + 24q^{70} + 208q^{72} + 20q^{73} + 88q^{76} - 186q^{78} + 44q^{79} + 56q^{81} + 140q^{82} - 242q^{84} + 16q^{85} - 232q^{87} - 284q^{93} - 60q^{94} + 26q^{96} - 264q^{99} + O(q^{100})$$

## 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.s.a $$160$$ $$2.755$$ None $$0$$ $$0$$ $$-16$$ $$0$$
345.2.s.b $$160$$ $$2.755$$ None $$0$$ $$0$$ $$16$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(345, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(69, [\chi])$$$$^{\oplus 2}$$