# Properties

 Label 195.2.v Level $195$ Weight $2$ Character orbit 195.v Rep. character $\chi_{195}(4,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $32$ Newform subspaces $1$ Sturm bound $56$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$195 = 3 \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 195.v (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$65$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$56$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(195, [\chi])$$.

Total New Old
Modular forms 64 32 32
Cusp forms 48 32 16
Eisenstein series 16 0 16

## Trace form

 $$32q - 20q^{4} + 16q^{9} + O(q^{10})$$ $$32q - 20q^{4} + 16q^{9} + 2q^{10} - 12q^{11} + 8q^{14} - 6q^{15} - 28q^{16} - 30q^{20} - 4q^{25} + 52q^{26} - 24q^{29} + 4q^{30} - 2q^{35} + 20q^{36} + 4q^{40} - 36q^{41} + 12q^{45} - 48q^{46} - 28q^{49} + 54q^{50} - 40q^{51} + 24q^{55} - 56q^{56} + 84q^{59} - 32q^{61} + 136q^{64} + 20q^{65} + 8q^{66} - 24q^{69} + 12q^{71} + 40q^{74} - 16q^{75} + 48q^{76} - 104q^{79} + 66q^{80} - 16q^{81} - 48q^{84} - 54q^{85} - 48q^{89} + 4q^{90} + 12q^{91} - 8q^{94} + 12q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(195, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
195.2.v.a $$32$$ $$1.557$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(195, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(195, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 2}$$