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

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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:
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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 \(S_{2}^{\mathrm{new}}(945, [\chi])\).