Newform orbit 230.2.l.a

• Label: 230.2.l.a
• Level: $230$
• Weight: $2$
• Character orbit: 230.l
• Analytic conductor: $1.837$
• Analytic rank: $0$
• Dimension: $240$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.83655924649\)
Analytic rank:	\(0\)
Dimension:	\(240\)
Relative dimension:	\(12\) over \(\Q(\zeta_{44})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
7.1	−0.997452	+	0.0713392i	−0.666533	+	3.06400i	0.989821	−	0.142315i	−0.533993	+	2.17137i	0.446251	−	3.10375i	−1.50098	+	2.74884i	−0.977147	+	0.212565i	−6.21495	−	2.83827i	0.377729	−	2.20393i
7.2	−0.997452	+	0.0713392i	−0.442321	+	2.03332i	0.989821	−	0.142315i	1.86221	−	1.23780i	0.296139	−	2.05969i	1.88657	−	3.45500i	−0.977147	+	0.212565i	−1.20984	−	0.552516i	−1.76917	+	1.36750i
7.3	−0.997452	+	0.0713392i	−0.293712	+	1.35017i	0.989821	−	0.142315i	−2.12582	−	0.693460i	0.196644	−	1.36769i	−0.324076	+	0.593501i	−0.977147	+	0.212565i	0.992195	+	0.453120i	2.16988	+	0.540039i
7.4	−0.997452	+	0.0713392i	−0.0823325	+	0.378476i	0.989821	−	0.142315i	−0.0392167	+	2.23572i	0.0551225	−	0.383386i	1.43832	−	2.63408i	−0.977147	+	0.212565i	2.59243	+	1.18392i	−0.120378	−	2.23283i
7.5	−0.997452	+	0.0713392i	0.184045	−	0.846041i	0.989821	−	0.142315i	2.13522	+	0.663941i	−0.123220	+	0.857015i	−2.12852	+	3.89809i	−0.977147	+	0.212565i	2.04698	+	0.934826i	−2.17715	−	0.509924i
7.6	−0.997452	+	0.0713392i	0.445581	−	2.04831i	0.989821	−	0.142315i	0.313060	−	2.21404i	−0.298322	+	2.07487i	0.390085	−	0.714388i	−0.977147	+	0.212565i	−1.26811	−	0.579129i	−0.154315	+	2.23074i
7.7	0.997452	−	0.0713392i	−0.664372	+	3.05407i	0.989821	−	0.142315i	2.09578	+	0.779553i	−0.444805	+	3.09368i	1.24726	−	2.28419i	0.977147	−	0.212565i	−6.15705	−	2.81183i	2.14605	+	0.628055i
7.8	0.997452	−	0.0713392i	−0.372248	+	1.71120i	0.989821	−	0.142315i	−2.13965	+	0.649526i	−0.249224	+	1.73339i	−1.73066	+	3.16947i	0.977147	−	0.212565i	−0.0607343	−	0.0277364i	−2.08786	+	0.800513i
7.9	0.997452	−	0.0713392i	−0.307156	+	1.41198i	0.989821	−	0.142315i	1.55520	−	1.60666i	−0.205645	+	1.43029i	−1.84581	+	3.38035i	0.977147	−	0.212565i	0.829567	+	0.378851i	1.43661	−	1.71352i
7.10	0.997452	−	0.0713392i	0.0484278	−	0.222619i	0.989821	−	0.142315i	−0.464445	+	2.18730i	0.0324229	−	0.225507i	1.13968	−	2.08717i	0.977147	−	0.212565i	2.68168	+	1.22468i	−0.307222	+	2.21486i
7.11	0.997452	−	0.0713392i	0.452602	−	2.08058i	0.989821	−	0.142315i	−1.62540	−	1.53561i	0.303022	−	2.10757i	−0.567213	+	1.03877i	0.977147	−	0.212565i	−1.39507	−	0.637105i	−1.73080	−	1.41574i
7.12	0.997452	−	0.0713392i	0.544276	−	2.50200i	0.989821	−	0.142315i	2.18999	+	0.451614i	0.364399	−	2.53445i	−0.470705	+	0.862032i	0.977147	−	0.212565i	−3.23486	−	1.47731i	2.21663	+	0.294232i
17.1	−0.936950	+	0.349464i	−2.43530	+	1.32977i	0.755750	−	0.654861i	2.05188	−	0.888703i	1.81704	−	2.09698i	−1.58597	−	2.11861i	−0.479249	+	0.877679i	2.54045	−	3.95301i	−1.61194	+	1.54973i
17.2	−0.936950	+	0.349464i	−1.69758	+	0.926949i	0.755750	−	0.654861i	−1.50435	+	1.65436i	1.26661	−	1.46175i	−0.735871	−	0.983009i	−0.479249	+	0.877679i	0.400622	−	0.623380i	0.831363	−	2.07577i
17.3	−0.936950	+	0.349464i	−0.565213	+	0.308630i	0.755750	−	0.654861i	−1.72918	−	1.41772i	0.421721	−	0.486692i	1.82117	+	2.43280i	−0.479249	+	0.877679i	−1.39771	+	2.17488i	2.11560	+	0.724045i
17.4	−0.936950	+	0.349464i	1.26604	−	0.691312i	0.755750	−	0.654861i	−0.584903	+	2.15821i	−0.944630	+	1.09016i	1.35459	+	1.80952i	−0.479249	+	0.877679i	−0.496969	+	0.773299i	−0.206194	−	2.22654i
17.5	−0.936950	+	0.349464i	1.92611	−	1.05174i	0.755750	−	0.654861i	2.14017	−	0.647831i	−1.43713	+	1.65853i	0.903621	+	1.20710i	−0.479249	+	0.877679i	0.981834	−	1.52776i	−1.77883	+	1.35490i
17.6	−0.936950	+	0.349464i	2.58843	−	1.41339i	0.755750	−	0.654861i	−2.20870	−	0.348772i	−1.93130	+	2.22883i	−2.57783	−	3.44357i	−0.479249	+	0.877679i	3.08036	−	4.79313i	2.19132	−	0.445080i
17.7	0.936950	−	0.349464i	−1.94498	+	1.06204i	0.755750	−	0.654861i	−1.77597	−	1.35866i	−1.45120	+	1.67478i	−3.01546	−	4.02819i	0.479249	−	0.877679i	1.03309	−	1.60752i	−2.13879	−	0.652357i
17.8	0.936950	−	0.349464i	−1.76120	+	0.961687i	0.755750	−	0.654861i	−1.99344	+	1.01301i	−1.31408	+	1.51653i	2.41169	+	3.22164i	0.479249	−	0.877679i	0.555057	−	0.863686i	−1.51374	+	1.64578i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
23.d	odd	22	1	inner
115.l	even	44	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	230.2.l.a	✓	240
5.c	odd	4	1	inner	230.2.l.a	✓	240
23.d	odd	22	1	inner	230.2.l.a	✓	240
115.l	even	44	1	inner	230.2.l.a	✓	240

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
230.2.l.a	✓	240	1.a	even	1	1	trivial
230.2.l.a	✓	240	5.c	odd	4	1	inner
230.2.l.a	✓	240	23.d	odd	22	1	inner
230.2.l.a	✓	240	115.l	even	44	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(230, [\chi])\).