# Properties

 Label 230.3.c.a Level $230$ Weight $3$ Character orbit 230.c Analytic conductor $6.267$ Analytic rank $0$ Dimension $24$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$230 = 2 \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 230.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.26704608029$$ Analytic rank: $$0$$ Dimension: $$24$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## $q$-expansion

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

 $$\operatorname{Tr}(f)(q) =$$ $$24q - 48q^{4} + 8q^{6} - 96q^{9} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$24q - 48q^{4} + 8q^{6} - 96q^{9} + 96q^{16} - 16q^{24} - 48q^{25} - 32q^{26} + 100q^{29} - 124q^{31} - 28q^{35} + 192q^{36} + 192q^{39} - 116q^{41} + 148q^{46} - 76q^{49} - 144q^{50} - 16q^{54} - 224q^{55} + 84q^{59} - 192q^{64} - 340q^{69} + 328q^{70} + 196q^{71} - 496q^{75} + 1360q^{81} + 316q^{85} - 376q^{94} - 368q^{95} + 32q^{96} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
229.1 1.41421i 5.45221i −2.00000 −3.90521 + 3.12239i −7.71059 0.770899 2.82843i −20.7266 4.41573 + 5.52280i
229.2 1.41421i 5.45221i −2.00000 3.90521 3.12239i −7.71059 −0.770899 2.82843i −20.7266 −4.41573 5.52280i
229.3 1.41421i 2.29017i −2.00000 −2.28201 4.44887i −3.23879 −9.92340 2.82843i 3.75511 −6.29165 + 3.22725i
229.4 1.41421i 2.29017i −2.00000 2.28201 + 4.44887i −3.23879 9.92340 2.82843i 3.75511 6.29165 3.22725i
229.5 1.41421i 0.894518i −2.00000 −3.14390 + 3.88792i −1.26504 −4.24317 2.82843i 8.19984 5.49835 + 4.44614i
229.6 1.41421i 0.894518i −2.00000 3.14390 3.88792i −1.26504 4.24317 2.82843i 8.19984 −5.49835 4.44614i
229.7 1.41421i 1.47600i −2.00000 −4.75172 + 1.55601i 2.08738 0.788814 2.82843i 6.82142 2.20053 + 6.71994i
229.8 1.41421i 1.47600i −2.00000 4.75172 1.55601i 2.08738 −0.788814 2.82843i 6.82142 −2.20053 6.71994i
229.9 1.41421i 3.00625i −2.00000 −3.95888 3.05405i 4.25149 7.53698 2.82843i −0.0375672 −4.31908 + 5.59871i
229.10 1.41421i 3.00625i −2.00000 3.95888 + 3.05405i 4.25149 −7.53698 2.82843i −0.0375672 4.31908 5.59871i
229.11 1.41421i 5.56886i −2.00000 −0.637273 + 4.95922i 7.87556 10.0249 2.82843i −22.0122 7.01340 + 0.901240i
229.12 1.41421i 5.56886i −2.00000 0.637273 4.95922i 7.87556 −10.0249 2.82843i −22.0122 −7.01340 0.901240i
229.13 1.41421i 5.56886i −2.00000 −0.637273 4.95922i 7.87556 10.0249 2.82843i −22.0122 7.01340 0.901240i
229.14 1.41421i 5.56886i −2.00000 0.637273 + 4.95922i 7.87556 −10.0249 2.82843i −22.0122 −7.01340 + 0.901240i
229.15 1.41421i 3.00625i −2.00000 −3.95888 + 3.05405i 4.25149 7.53698 2.82843i −0.0375672 −4.31908 5.59871i
229.16 1.41421i 3.00625i −2.00000 3.95888 3.05405i 4.25149 −7.53698 2.82843i −0.0375672 4.31908 + 5.59871i
229.17 1.41421i 1.47600i −2.00000 −4.75172 1.55601i 2.08738 0.788814 2.82843i 6.82142 2.20053 6.71994i
229.18 1.41421i 1.47600i −2.00000 4.75172 + 1.55601i 2.08738 −0.788814 2.82843i 6.82142 −2.20053 + 6.71994i
229.19 1.41421i 0.894518i −2.00000 −3.14390 3.88792i −1.26504 −4.24317 2.82843i 8.19984 5.49835 4.44614i
229.20 1.41421i 0.894518i −2.00000 3.14390 + 3.88792i −1.26504 4.24317 2.82843i 8.19984 −5.49835 + 4.44614i
See all 24 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 229.24 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
23.b odd 2 1 inner
115.c odd 2 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 230.3.c.a 24
5.b even 2 1 inner 230.3.c.a 24
5.c odd 4 2 1150.3.d.e 24
23.b odd 2 1 inner 230.3.c.a 24
115.c odd 2 1 inner 230.3.c.a 24
115.e even 4 2 1150.3.d.e 24

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
230.3.c.a 24 1.a even 1 1 trivial
230.3.c.a 24 5.b even 2 1 inner
230.3.c.a 24 23.b odd 2 1 inner
230.3.c.a 24 115.c odd 2 1 inner
1150.3.d.e 24 5.c odd 4 2
1150.3.d.e 24 115.e even 4 2

## Hecke kernels

This newform subspace is the entire newspace $$S_{3}^{\mathrm{new}}(230, [\chi])$$.