Newform orbit 184.4.p.a

• Label: 184.4.p.a
• Level: $184$
• Weight: $4$
• Character orbit: 184.p
• Analytic conductor: $10.856$
• Analytic rank: $0$
• Dimension: $700$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 184 = 2^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	184.p (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(10.8563514411\)
Analytic rank:	\(0\)
Dimension:	\(700\)
Relative dimension:	\(70\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 700 q - 7 q^{2} + 13 q^{4} - 52 q^{6} + 10 q^{7} - 46 q^{8} + 576 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
13.1	−2.82177	−	0.194003i	4.65932	−	7.25004i	7.92473	+	1.09486i	8.29174	+	3.78671i	−14.5540	+	19.5540i	−11.4299	−	3.35613i	−22.1493	−	4.62687i	−19.6376	−	43.0004i	−22.6627	−	12.2938i
13.2	−2.79214	+	0.451587i	−0.319292	+	0.496829i	7.59214	−	2.52179i	−11.7845	−	5.38181i	0.667149	−	1.53141i	16.5509	+	4.85977i	−20.0595	+	10.4697i	11.0713	+	24.2428i	35.3344	+	9.70505i
13.3	−2.78899	−	0.470655i	2.10434	−	3.27441i	7.55697	+	2.62531i	−15.6342	−	7.13988i	−7.41010	+	8.14189i	−26.5644	−	7.80002i	−19.8407	−	10.8787i	4.92267	+	10.7791i	40.2431	+	27.2714i
13.4	−2.78868	+	0.472533i	0.211978	−	0.329845i	7.55342	−	2.63548i	19.1446	+	8.74304i	−0.435276	+	1.02000i	13.8917	+	4.07896i	−19.8187	+	10.9188i	11.1523	+	24.4202i	−57.5194	−	15.3350i
13.5	−2.75607	+	0.635667i	−3.45705	+	5.37928i	7.19186	−	3.50389i	0.666625	+	0.304437i	6.10845	−	17.0232i	2.44044	+	0.716579i	−17.5940	+	14.2286i	−5.76921	−	12.6328i	−2.03079	−	0.415299i
13.6	−2.73301	−	0.728461i	−3.83843	+	5.97271i	6.93869	+	3.98178i	6.77757	+	3.09521i	14.8414	−	13.5273i	−22.8169	−	6.69964i	−16.0629	−	15.9368i	−9.72355	−	21.2916i	−16.2684	−	13.3964i
13.7	−2.66562	−	0.945759i	−0.742667	+	1.15561i	6.21108	+	5.04207i	−4.31259	−	1.96949i	3.07260	−	2.37804i	−0.499324	−	0.146615i	−11.7878	−	19.3144i	10.4323	+	22.8436i	9.63307	+	9.32859i
13.8	−2.63504	+	1.02790i	1.20289	−	1.87173i	5.88684	−	5.41711i	5.36058	+	2.44809i	−1.24570	+	6.16853i	−21.1082	−	6.19793i	−9.94379	+	20.3254i	9.15977	+	20.0571i	−16.6417	−	0.940677i
13.9	−2.63392	−	1.03076i	3.26185	−	5.07553i	5.87507	+	5.42988i	0.857807	+	0.391747i	−13.8231	+	10.0064i	19.3203	+	5.67294i	−9.87756	−	20.3576i	−3.90518	−	8.55114i	−1.85560	−	1.91602i
13.10	−2.59696	−	1.12062i	−5.54497	+	8.62814i	5.48844	+	5.82040i	−17.2752	−	7.88933i	24.0689	−	16.1932i	24.2631	+	7.12429i	−7.73083	−	21.2658i	−32.4819	−	71.1255i	36.0222	+	39.8472i
13.11	−2.51211	+	1.29974i	4.77251	−	7.42617i	4.62138	−	6.53015i	−15.5465	−	7.09987i	−2.33700	+	24.8583i	3.24534	+	0.952919i	−3.12192	+	22.4110i	−21.1549	−	46.3228i	48.2826	−	2.37076i
13.12	−2.45818	−	1.39905i	−1.32741	+	2.06550i	4.08534	+	6.87823i	11.4759	+	5.24089i	6.15276	−	3.22026i	30.0246	+	8.81603i	−0.419555	−	22.6235i	8.71195	+	19.0765i	−20.8777	−	28.9384i
13.13	−2.33635	+	1.59421i	3.48281	−	5.41936i	2.91702	−	7.44923i	4.59069	+	2.09650i	0.502522	+	18.2138i	14.2736	+	4.19111i	5.06043	+	22.0543i	−6.02331	−	13.1892i	−14.0677	+	2.42036i
13.14	−2.31497	+	1.62509i	−4.76362	+	7.41234i	2.71817	−	7.52406i	11.6365	+	5.31419i	−1.01807	−	24.9006i	6.99300	+	2.05333i	5.93478	+	21.8353i	−21.0345	−	46.0590i	−35.5741	+	6.60808i
13.15	−2.18449	+	1.79666i	−3.91352	+	6.08955i	1.54403	−	7.84958i	−18.3355	−	8.37356i	−2.39179	−	20.3338i	−28.2836	−	8.30480i	10.7301	+	19.9215i	−10.5508	−	23.1030i	55.0983	−	14.6507i
13.16	−2.14354	+	1.84532i	0.182132	−	0.283403i	1.18957	−	7.91106i	2.56171	+	1.16989i	0.132562	+	0.943579i	−29.8765	−	8.77253i	12.0486	+	19.1529i	11.1691	+	24.4568i	−7.64996	+	2.21946i
13.17	−2.03122	−	1.96829i	4.41866	−	6.87557i	0.251690	+	7.99604i	−15.8545	−	7.24050i	−22.5084	+	5.26859i	11.0008	+	3.23011i	15.2273	−	16.7371i	−16.5327	−	36.2016i	17.9525	+	45.9132i
13.18	−1.99303	−	2.00694i	1.79904	−	2.79935i	−0.0556462	+	7.99981i	15.3703	+	7.01938i	−9.20368	+	1.96864i	−23.6044	−	6.93089i	16.1661	−	15.8322i	6.61635	+	14.4878i	−16.5460	−	44.8372i
13.19	−1.92778	−	2.06970i	2.56070	−	3.98452i	−0.567302	+	7.97986i	3.69553	+	1.68769i	−13.1832	+	2.38142i	−4.06261	−	1.19289i	17.6095	−	14.2093i	1.89697	+	4.15377i	−3.63117	−	10.9021i
13.20	−1.81307	+	2.17089i	−2.96299	+	4.61050i	−1.42554	−	7.87196i	−5.39160	−	2.46226i	−4.63679	−	14.7915i	30.7524	+	9.02973i	19.6738	+	11.1777i	−1.26121	−	2.76167i	15.1207	−	7.24033i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
8.b	even	2	1	inner
23.c	even	11	1	inner
184.p	even	22	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	184.4.p.a	✓	700
8.b	even	2	1	inner	184.4.p.a	✓	700
23.c	even	11	1	inner	184.4.p.a	✓	700
184.p	even	22	1	inner	184.4.p.a	✓	700

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
184.4.p.a	✓	700	1.a	even	1	1	trivial
184.4.p.a	✓	700	8.b	even	2	1	inner
184.4.p.a	✓	700	23.c	even	11	1	inner
184.4.p.a	✓	700	184.p	even	22	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(184, [\chi])\).