# Properties

 Label 95.5.d Level $95$ Weight $5$ Character orbit 95.d Rep. character $\chi_{95}(94,\cdot)$ Character field $\Q$ Dimension $38$ Newform subspaces $5$ Sturm bound $50$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$95 = 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$5$$ Character orbit: $$[\chi]$$ $$=$$ 95.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$95$$ Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$50$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(95, [\chi])$$.

Total New Old
Modular forms 42 42 0
Cusp forms 38 38 0
Eisenstein series 4 4 0

## Trace form

 $$38 q + 256 q^{4} - 11 q^{5} - 104 q^{6} + 914 q^{9} + O(q^{10})$$ $$38 q + 256 q^{4} - 11 q^{5} - 104 q^{6} + 914 q^{9} + 110 q^{11} + 2008 q^{16} - 266 q^{19} - 2148 q^{20} + 416 q^{24} - 347 q^{25} + 3280 q^{26} - 816 q^{30} + 75 q^{35} + 320 q^{36} + 4024 q^{39} - 6912 q^{44} + 2547 q^{45} - 15012 q^{49} - 3696 q^{54} + 8993 q^{55} - 5786 q^{61} + 2568 q^{64} - 27960 q^{66} + 48064 q^{74} - 30840 q^{76} - 45112 q^{80} - 22698 q^{81} + 28785 q^{85} + 35233 q^{95} + 79712 q^{96} + 25666 q^{99} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(95, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
95.5.d.a $2$ $9.820$ $$\Q(\sqrt{-19})$$ $$\Q(\sqrt{-19})$$ $$0$$ $$0$$ $$31$$ $$0$$ $$q-2^{4}q^{4}+(14+3\beta )q^{5}+(5-10\beta )q^{7}+\cdots$$
95.5.d.b $2$ $9.820$ $$\Q(\sqrt{19})$$ $$\Q(\sqrt{-95})$$ $$0$$ $$0$$ $$50$$ $$0$$ $$q+\beta q^{2}-4\beta q^{3}+3q^{4}+5^{2}q^{5}-76q^{6}+\cdots$$
95.5.d.c $2$ $9.820$ $$\Q(\sqrt{5})$$ $$\Q(\sqrt{-95})$$ $$0$$ $$0$$ $$50$$ $$0$$ $$q-3\beta q^{2}-2\beta q^{3}+29q^{4}+5^{2}q^{5}+\cdots$$
95.5.d.d $4$ $9.820$ $$\Q(\sqrt{10}, \sqrt{38})$$ $$\Q(\sqrt{-95})$$ $$0$$ $$0$$ $$-100$$ $$0$$ $$q+(\beta _{1}+\beta _{2})q^{2}+(4\beta _{1}-3\beta _{2})q^{3}+(2^{4}+\cdots)q^{4}+\cdots$$
95.5.d.e $28$ $9.820$ None $$0$$ $$0$$ $$-42$$ $$0$$