# Properties

 Label 95.2.b Level $95$ Weight $2$ Character orbit 95.b Rep. character $\chi_{95}(39,\cdot)$ Character field $\Q$ Dimension $8$ 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.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ 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 12 8 4
Cusp forms 8 8 0
Eisenstein series 4 0 4

## Trace form

 $$8 q - 6 q^{4} - 3 q^{5} - 8 q^{9} + O(q^{10})$$ $$8 q - 6 q^{4} - 3 q^{5} - 8 q^{9} + 8 q^{10} - 6 q^{11} - 12 q^{14} + 10 q^{15} - 6 q^{16} + 4 q^{19} + 8 q^{20} + 20 q^{21} - 8 q^{24} - 3 q^{25} + 12 q^{26} - 24 q^{29} + 24 q^{30} - 8 q^{31} + 16 q^{34} + 5 q^{35} - 26 q^{36} + 8 q^{39} - 4 q^{40} - 8 q^{41} - 28 q^{44} - 21 q^{45} + 4 q^{46} + 10 q^{49} + 4 q^{50} + 4 q^{51} + 16 q^{54} - 25 q^{55} + 52 q^{56} - 20 q^{59} + 20 q^{60} - 10 q^{61} - 2 q^{64} - 12 q^{65} - 48 q^{66} + 24 q^{69} + 16 q^{70} + 60 q^{71} + 20 q^{74} - 34 q^{75} - 10 q^{76} + 16 q^{79} - 30 q^{80} + 56 q^{81} + 24 q^{84} + 29 q^{85} - 20 q^{86} - 20 q^{89} - 40 q^{90} - 32 q^{91} + 36 q^{94} + q^{95} - 64 q^{96} + 6 q^{99} + O(q^{100})$$

## 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.b.a $2$ $0.759$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{2}+q^{4}+(-1+2i)q^{5}-2iq^{7}+\cdots$$
95.2.b.b $6$ $0.759$ 6.0.16516096.1 None $$0$$ $$0$$ $$-1$$ $$0$$ $$q-\beta _{5}q^{2}+(-\beta _{1}+\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots$$