Newform orbit 112.4.v.a

• Label: 112.4.v.a
• Level: $112$
• Weight: $4$
• Character orbit: 112.v
• Analytic conductor: $6.608$
• Analytic rank: $0$
• Dimension: $184$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	112.v (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.60821392064\)
Analytic rank:	\(0\)
Dimension:	\(184\)
Relative dimension:	\(46\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 184 q - 2 q^{2} - 6 q^{3} - 12 q^{4} - 6 q^{5} - 8 q^{7} - 92 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3.1	−2.82839	+	0.0141260i	5.51747	−	1.47840i	7.99960	−	0.0799080i	−4.40582	+	16.4428i	−15.5847	+	4.25944i	−17.8423	+	4.96514i	−22.6249	+	0.339014i	4.87413	−	2.81408i	12.2291	−	46.5688i
3.2	−2.82797	−	0.0507430i	−0.465372	+	0.124696i	7.99485	+	0.287000i	4.77994	−	17.8390i	1.32239	−	0.329023i	15.8112	+	9.64399i	−22.5946	−	1.21731i	−23.1817	+	13.3839i	−14.4227	+	50.2056i
3.3	−2.78312	−	0.504203i	9.51873	−	2.55054i	7.49156	+	2.80652i	1.99907	−	7.46064i	−27.7778	+	2.29909i	14.4692	−	11.5604i	−19.4349	−	11.5882i	60.7182	−	35.0557i	−9.32534	+	19.7559i
3.4	−2.77698	−	0.537021i	−5.80523	+	1.55551i	7.42322	+	2.98259i	1.48510	−	5.54245i	16.9563	−	1.20208i	−15.7717	−	9.70839i	−19.0124	−	12.2690i	7.89837	−	4.56013i	−7.10049	+	14.5937i
3.5	−2.76232	+	0.607948i	−5.74189	+	1.53854i	7.26080	−	3.35869i	−2.16392	+	8.07584i	14.9256	−	7.74070i	−3.83072	+	18.1198i	−18.0147	+	13.6920i	7.21955	−	4.16821i	1.06773	−	23.6236i
3.6	−2.66116	+	0.958254i	2.15679	−	0.577911i	6.16350	−	5.10013i	−2.32709	+	8.68481i	−5.18578	+	3.60467i	15.7307	−	9.77476i	−11.5148	+	19.4784i	−19.0649	+	11.0071i	−2.12951	−	25.3416i
3.7	−2.46946	−	1.37904i	−5.24368	+	1.40504i	4.19650	+	6.81097i	−4.79126	+	17.8812i	14.8867	+	3.76154i	17.2319	−	6.78680i	−0.970524	−	22.6066i	2.13935	−	1.23515i	36.4907	−	37.5497i
3.8	−2.36860	+	1.54588i	1.91427	−	0.512927i	3.22050	−	7.32314i	3.00477	−	11.2139i	−3.74121	+	4.17415i	−14.8682	−	11.0425i	3.69262	+	22.3241i	−19.9814	+	11.5362i	10.2183	+	31.2063i
3.9	−2.36026	+	1.55858i	−9.22721	+	2.47242i	3.14164	−	7.35731i	1.13789	−	4.24665i	17.9251	−	20.2169i	15.0595	−	10.7801i	4.05189	+	22.2617i	55.6459	−	32.1272i	3.93305	+	11.7967i
3.10	−2.32317	−	1.61335i	2.10770	−	0.564756i	2.79422	+	7.49615i	0.330327	−	1.23280i	−5.80768	−	2.08842i	−0.114936	+	18.5199i	5.60244	−	21.9229i	−19.2592	+	11.1193i	−2.75634	+	2.33106i
3.11	−2.24441	−	1.72122i	4.24184	−	1.13660i	2.07480	+	7.72627i	−0.268296	+	1.00130i	−11.4768	−	4.75015i	−7.71253	−	16.8380i	8.64191	−	20.9121i	−6.68131	+	3.85746i	2.32562	−	1.78552i
3.12	−2.11245	+	1.88083i	8.09590	−	2.16929i	0.924921	−	7.94635i	0.760966	−	2.83997i	−13.0221	+	19.8096i	−0.764983	+	18.5045i	12.9919	+	18.5259i	37.4551	−	21.6247i	3.73400	+	7.43055i
3.13	−1.55961	+	2.35958i	−4.16910	+	1.11711i	−3.13526	−	7.36004i	−4.19765	+	15.6659i	3.86625	−	11.5796i	−15.5278	−	10.0939i	22.2564	+	4.08087i	−7.24920	+	4.18533i	−30.4182	−	34.3373i
3.14	−1.55033	−	2.36568i	−4.30152	+	1.15259i	−3.19293	+	7.33520i	4.84665	−	18.0879i	9.39545	+	8.38913i	7.69015	−	16.8482i	22.3029	−	3.81856i	−6.20811	+	3.58425i	−50.3043	+	16.5767i
3.15	−1.42030	−	2.44596i	−7.81325	+	2.09355i	−3.96548	+	6.94802i	−0.364872	+	1.36172i	16.2179	+	16.1375i	−14.0821	+	12.0289i	22.6268	−	0.168861i	33.2813	−	19.2149i	3.84895	−	1.04159i
3.16	−1.38573	+	2.46572i	−5.17149	+	1.38570i	−4.15952	−	6.83362i	3.74208	−	13.9656i	3.74954	−	14.6716i	−5.34252	+	17.7329i	22.6137	−	0.786667i	1.44147	−	0.832230i	29.2498	+	28.5795i
3.17	−1.17842	+	2.57125i	1.24986	−	0.334900i	−5.22266	−	6.06002i	−1.95056	+	7.27959i	−0.611751	+	3.60837i	16.7977	+	7.79973i	21.7363	−	6.28753i	−21.9327	+	12.6628i	−16.4191	−	13.5938i
3.18	−1.00251	−	2.64480i	8.82251	−	2.36398i	−5.98993	+	5.30290i	−4.23385	+	15.8010i	−15.0970	−	20.9638i	12.1308	+	13.9944i	20.0301	+	10.5259i	48.8655	−	28.2125i	46.0349	−	4.64299i
3.19	−0.916906	−	2.67568i	7.46808	−	2.00107i	−6.31857	+	4.90670i	5.67317	−	21.1726i	−12.2017	−	18.1474i	−17.1918	+	6.88781i	18.9223	+	12.4075i	28.3853	−	16.3882i	−61.8528	+	4.23364i
3.20	−0.637599	−	2.75562i	2.61044	−	0.699465i	−7.18693	+	3.51397i	−2.91295	+	10.8713i	−3.59188	−	6.74741i	−6.19460	−	17.4536i	14.2656	+	17.5640i	−17.0575	+	9.84817i	31.8145	+	1.09548i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.d	odd	6	1	inner
16.f	odd	4	1	inner
112.v	even	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	112.4.v.a	✓	184
7.d	odd	6	1	inner	112.4.v.a	✓	184
16.f	odd	4	1	inner	112.4.v.a	✓	184
112.v	even	12	1	inner	112.4.v.a	✓	184

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
112.4.v.a	✓	184	1.a	even	1	1	trivial
112.4.v.a	✓	184	7.d	odd	6	1	inner
112.4.v.a	✓	184	16.f	odd	4	1	inner
112.4.v.a	✓	184	112.v	even	12	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(112, [\chi])\).