# Properties

 Label 95.11.d Level $95$ Weight $11$ Character orbit 95.d Rep. character $\chi_{95}(94,\cdot)$ Character field $\Q$ Dimension $98$ Newform subspaces $4$ Sturm bound $110$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$95 = 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$11$$ Character orbit: $$[\chi]$$ $$=$$ 95.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$95$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$110$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{11}(95, [\chi])$$.

Total New Old
Modular forms 102 102 0
Cusp forms 98 98 0
Eisenstein series 4 4 0

## Trace form

 $$98 q + 50368 q^{4} + 1109 q^{5} + 760 q^{6} + 1850198 q^{9} + O(q^{10})$$ $$98 q + 50368 q^{4} + 1109 q^{5} + 760 q^{6} + 1850198 q^{9} - 130594 q^{11} + 23321368 q^{16} + 1528858 q^{19} + 6645180 q^{20} + 44844320 q^{24} - 8375915 q^{25} + 40029520 q^{26} - 45441744 q^{30} - 116436889 q^{35} + 973007168 q^{36} + 134353720 q^{39} - 1010104704 q^{44} - 160483077 q^{45} - 3999481056 q^{49} + 841666800 q^{54} - 1168252963 q^{55} - 1029741434 q^{61} + 7397052168 q^{64} - 3543457560 q^{66} - 14144890080 q^{74} + 18081554088 q^{76} + 10812290056 q^{80} + 38605570578 q^{81} - 11624327715 q^{85} - 1965704127 q^{95} + 12794582240 q^{96} - 83582806574 q^{99} + O(q^{100})$$

## Decomposition of $$S_{11}^{\mathrm{new}}(95, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
95.11.d.a $2$ $60.359$ $$\Q(\sqrt{-19})$$ $$\Q(\sqrt{-19})$$ $$0$$ $$0$$ $$3951$$ $$0$$ $$q-2^{10}q^{4}+(2026+101\beta )q^{5}+(177+\cdots)q^{7}+\cdots$$
95.11.d.b $4$ $60.359$ 4.4.462080.1 $$\Q(\sqrt{-95})$$ $$0$$ $$0$$ $$-12500$$ $$0$$ $$q+(\beta _{1}+12\beta _{2})q^{2}+(-23\beta _{1}+43\beta _{2}+\cdots)q^{3}+\cdots$$
95.11.d.c $4$ $60.359$ 4.4.7600.1 $$\Q(\sqrt{-95})$$ $$0$$ $$0$$ $$12500$$ $$0$$ $$q+(\beta _{1}+2\beta _{2})q^{2}+(-6\beta _{1}+17\beta _{2})q^{3}+\cdots$$
95.11.d.d $88$ $60.359$ None $$0$$ $$0$$ $$-2842$$ $$0$$