# Properties

 Label 945.2.cs.a Level 945 Weight 2 Character orbit 945.cs Analytic conductor 7.546 Analytic rank 0 Dimension 24 CM disc. -35

# Related objects

## Newspace parameters

 Level: $$N$$ = $$945 = 3^{3} \cdot 5 \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 945.cs (of order $$18$$ and degree $$6$$)

## Newform invariants

 Self dual: No Analytic conductor: $$7.54586299101$$ Analytic rank: $$0$$ Dimension: $$24$$ Relative dimension: $$4$$ over $$\Q(\zeta_{18})$$ Sato-Tate group: $\mathrm{U}(1)[D_{18}]$

## $q$-expansion

The dimension is sufficiently large that we do not compute an algebraic $$q$$-expansion, but we have computed the trace expansion.

 $$\operatorname{Tr}(f)(q) =$$ $$24q$$ $$\mathstrut -\mathstrut 6q^{9}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$24q$$ $$\mathstrut -\mathstrut 6q^{9}$$ $$\mathstrut -\mathstrut 18q^{11}$$ $$\mathstrut -\mathstrut 24q^{39}$$ $$\mathstrut +\mathstrut 96q^{64}$$ $$\mathstrut -\mathstrut 180q^{65}$$ $$\mathstrut -\mathstrut 12q^{79}$$ $$\mathstrut +\mathstrut 102q^{81}$$ $$\mathstrut +\mathstrut 84q^{84}$$ $$\mathstrut +\mathstrut 60q^{85}$$ $$\mathstrut +\mathstrut 228q^{99}$$ $$\mathstrut +\mathstrut O(q^{100})$$

## Embeddings

For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.

For more information on an embedded modular form you can click on its label.

Label $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
104.1 0 −1.62968 0.586627i −1.53209 1.28558i −2.20210 0.388289i 0 2.02676 1.70066i 0 2.31174 + 1.91203i 0
104.2 0 −0.306808 + 1.70466i −1.53209 1.28558i −2.20210 0.388289i 0 −2.02676 + 1.70066i 0 −2.81174 1.04601i 0
104.3 0 0.306808 1.70466i −1.53209 1.28558i 2.20210 + 0.388289i 0 2.02676 1.70066i 0 −2.81174 1.04601i 0
104.4 0 1.62968 + 0.586627i −1.53209 1.28558i 2.20210 + 0.388289i 0 −2.02676 + 1.70066i 0 2.31174 + 1.91203i 0
209.1 0 −1.62968 + 0.586627i −1.53209 + 1.28558i −2.20210 + 0.388289i 0 2.02676 + 1.70066i 0 2.31174 1.91203i 0
209.2 0 −0.306808 1.70466i −1.53209 + 1.28558i −2.20210 + 0.388289i 0 −2.02676 1.70066i 0 −2.81174 + 1.04601i 0
209.3 0 0.306808 + 1.70466i −1.53209 + 1.28558i 2.20210 0.388289i 0 2.02676 + 1.70066i 0 −2.81174 + 1.04601i 0
209.4 0 1.62968 0.586627i −1.53209 + 1.28558i 2.20210 0.388289i 0 −2.02676 1.70066i 0 2.31174 1.91203i 0
419.1 0 −1.62968 0.586627i 1.87939 0.684040i 1.43732 1.71293i 0 −2.48619 0.904900i 0 2.31174 + 1.91203i 0
419.2 0 −0.306808 + 1.70466i 1.87939 0.684040i 1.43732 1.71293i 0 2.48619 + 0.904900i 0 −2.81174 1.04601i 0
419.3 0 0.306808 1.70466i 1.87939 0.684040i −1.43732 + 1.71293i 0 −2.48619 0.904900i 0 −2.81174 1.04601i 0
419.4 0 1.62968 + 0.586627i 1.87939 0.684040i −1.43732 + 1.71293i 0 2.48619 + 0.904900i 0 2.31174 + 1.91203i 0
524.1 0 −1.62968 + 0.586627i −0.347296 1.96962i 0.764780 2.10122i 0 0.459430 2.60556i 0 2.31174 1.91203i 0
524.2 0 −0.306808 1.70466i −0.347296 1.96962i 0.764780 2.10122i 0 −0.459430 + 2.60556i 0 −2.81174 + 1.04601i 0
524.3 0 0.306808 + 1.70466i −0.347296 1.96962i −0.764780 + 2.10122i 0 0.459430 2.60556i 0 −2.81174 + 1.04601i 0
524.4 0 1.62968 0.586627i −0.347296 1.96962i −0.764780 + 2.10122i 0 −0.459430 + 2.60556i 0 2.31174 1.91203i 0
734.1 0 −1.62968 0.586627i −0.347296 + 1.96962i 0.764780 + 2.10122i 0 0.459430 + 2.60556i 0 2.31174 + 1.91203i 0
734.2 0 −0.306808 + 1.70466i −0.347296 + 1.96962i 0.764780 + 2.10122i 0 −0.459430 2.60556i 0 −2.81174 1.04601i 0
734.3 0 0.306808 1.70466i −0.347296 + 1.96962i −0.764780 2.10122i 0 0.459430 + 2.60556i 0 −2.81174 1.04601i 0
734.4 0 1.62968 + 0.586627i −0.347296 + 1.96962i −0.764780 2.10122i 0 −0.459430 2.60556i 0 2.31174 + 1.91203i 0
See all 24 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 839.4 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Only self twists have been computed for this newform, which has CM by $$\Q(\sqrt{-35})$$.

## Hecke kernels

This newform can be constructed as the kernel of the linear operator $$T_{2}$$ acting on $$S_{2}^{\mathrm{new}}(945, [\chi])$$.