# Properties

 Label 95.2.i Level $95$ Weight $2$ Character orbit 95.i Rep. character $\chi_{95}(49,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $16$ Newform subspaces $2$ Sturm bound $20$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$95 = 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 95.i (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$95$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$20$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(95, [\chi])$$.

Total New Old
Modular forms 24 24 0
Cusp forms 16 16 0
Eisenstein series 8 8 0

## Trace form

 $$16 q + 6 q^{4} - 12 q^{6} + 2 q^{9} + O(q^{10})$$ $$16 q + 6 q^{4} - 12 q^{6} + 2 q^{9} - 2 q^{10} + 6 q^{14} - 4 q^{15} - 6 q^{16} + 2 q^{19} - 32 q^{20} - 20 q^{21} + 2 q^{24} - 60 q^{26} + 6 q^{29} + 12 q^{30} + 32 q^{31} + 2 q^{34} + 16 q^{35} + 26 q^{36} + 4 q^{39} + 10 q^{40} - 16 q^{41} + 16 q^{44} + 48 q^{45} + 56 q^{46} - 40 q^{49} - 40 q^{50} - 40 q^{51} - 4 q^{54} - 20 q^{55} + 92 q^{56} + 38 q^{59} + 4 q^{60} + 16 q^{61} + 56 q^{64} - 24 q^{65} - 6 q^{66} - 36 q^{69} + 62 q^{70} - 14 q^{74} - 56 q^{75} - 74 q^{76} + 26 q^{79} - 30 q^{80} - 32 q^{81} - 96 q^{84} + 10 q^{85} + 8 q^{86} + 14 q^{89} - 32 q^{90} + 8 q^{91} - 108 q^{94} + 62 q^{95} + 52 q^{96} - 24 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(95, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
95.2.i.a $4$ $0.759$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+\zeta_{12}q^{2}+2\zeta_{12}^{2}q^{4}+(1-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{5}+\cdots$$
95.2.i.b $12$ $0.759$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\beta _{5}q^{2}+(\beta _{4}-\beta _{5})q^{3}+(-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$$