Newform orbit 211.4.d.a

• Label: 211.4.d.a
• Level: $211$
• Weight: $4$
• Character orbit: 211.d
• Analytic conductor: $12.449$
• Analytic rank: $0$
• Dimension: $208$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 211 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	211.d (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(12.4494030112\)
Analytic rank:	\(0\)
Dimension:	\(208\)
Relative dimension:	\(52\) over \(\Q(\zeta_{5})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 208 q - 7 q^{2} - 6 q^{3} - 209 q^{4} - 3 q^{5} + 15 q^{6} - 47 q^{7} - 4 q^{8} - 360 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
55.1	−1.69954	−	5.23066i	7.27673	+	5.28685i	−17.9992	+	13.0772i	−1.22913	+	0.893014i	15.2866	−	47.0473i	4.73605	−	14.5761i	63.3971	+	46.0607i	16.6565	+	51.2635i	6.76001	+	4.91143i
55.2	−1.64462	−	5.06163i	−6.11186	−	4.44053i	−16.4432	+	11.9467i	1.27243	−	0.924477i	−12.4246	+	38.2390i	−2.01467	+	6.20052i	53.0669	+	38.5554i	9.29312	+	28.6013i	−6.77203	−	4.92017i
55.3	−1.63265	−	5.02477i	2.83668	+	2.06097i	−16.1106	+	11.7051i	14.8719	−	10.8051i	5.72459	−	17.6185i	−10.3445	+	31.8370i	50.9237	+	36.9982i	−4.54431	−	13.9859i	−78.5734	−	57.0869i
55.4	−1.58541	−	4.87939i	−1.68757	−	1.22609i	−14.8228	+	10.7694i	−14.4888	+	10.5267i	−3.30708	+	10.1782i	−0.170876	+	0.525902i	42.8429	+	31.1272i	−6.99887	−	21.5403i	74.3345	+	54.0072i
55.5	−1.54482	−	4.75447i	−0.579321	−	0.420901i	−13.7464	+	9.98732i	5.20679	−	3.78295i	−1.10621	+	3.40458i	7.41180	−	22.8112i	36.3649	+	26.4207i	−8.18500	−	25.1909i	−26.0295	−	18.9115i
55.6	−1.39405	−	4.29043i	2.29242	+	1.66554i	−9.99229	+	7.25983i	−1.51311	+	1.09934i	3.95015	−	12.1573i	−0.326626	+	1.00525i	15.8802	+	11.5377i	−5.86229	−	18.0423i	6.82596	+	4.95935i
55.7	−1.34331	−	4.13430i	−5.66575	−	4.11641i	−8.81577	+	6.40503i	16.2568	−	11.8113i	−9.40757	+	28.9535i	3.61459	−	11.1246i	10.1879	+	7.40196i	6.81245	+	20.9666i	−70.6693	−	51.3443i
55.8	−1.31336	−	4.04210i	4.95323	+	3.59873i	−8.14151	+	5.91515i	−11.0481	+	8.02690i	8.04106	−	24.7478i	0.700532	−	2.15602i	7.09501	+	5.15483i	3.24014	+	9.97212i	46.9556	+	34.1152i
55.9	−1.16374	−	3.58163i	−1.61978	−	1.17684i	−5.00162	+	3.63389i	3.94802	−	2.86840i	−2.33000	+	7.17101i	−6.40316	+	19.7069i	−5.53787	−	4.02350i	−7.10471	−	21.8661i	−14.8680	−	10.8023i
55.10	−1.12956	−	3.47644i	7.07930	+	5.14341i	−4.33756	+	3.15142i	−1.64128	+	1.19246i	9.88423	−	30.4205i	−8.58412	+	26.4192i	−7.80260	−	5.66892i	15.3183	+	47.1450i	5.99943	+	4.35884i
55.11	−1.12125	−	3.45085i	5.54645	+	4.02973i	−4.17900	+	3.03622i	13.6658	−	9.92879i	7.68704	−	23.6583i	5.16814	−	15.9059i	−8.32049	−	6.04519i	6.18091	+	19.0229i	−49.5855	−	36.0259i
55.12	−1.11107	−	3.41953i	−4.59927	−	3.34156i	−3.98659	+	2.89643i	−11.5818	+	8.41468i	−6.31647	+	19.4401i	−10.3701	+	31.9158i	−8.93679	−	6.49296i	1.64376	+	5.05898i	41.6426	+	30.2551i
55.13	−1.08998	−	3.35462i	−7.81328	−	5.67668i	−3.59325	+	2.61065i	−7.36173	+	5.34861i	−10.5268	+	32.3980i	1.88253	−	5.79383i	−10.1546	−	7.37771i	20.4792	+	63.0285i	25.9667	+	18.8659i
55.14	−1.06401	−	3.27469i	−3.77698	−	2.74414i	−3.11933	+	2.26633i	−3.92682	+	2.85301i	−4.96745	+	15.2882i	10.8080	−	33.2637i	−11.5444	−	8.38750i	−1.60815	−	4.94939i	13.5209	+	9.82350i
55.15	−0.866377	−	2.66643i	−5.16818	−	3.75490i	0.112877	−	0.0820098i	12.8215	−	9.31538i	−5.53461	+	17.0338i	0.621149	−	1.91170i	−18.4621	−	13.4135i	4.26734	+	13.1335i	−35.9471	−	26.1171i
55.16	−0.767001	−	2.36059i	−0.723259	−	0.525479i	1.48806	−	1.08114i	−15.8975	+	11.5502i	−0.685697	+	2.11036i	4.61945	−	14.2172i	−19.7577	−	14.3548i	−8.09648	−	24.9184i	39.4586	+	28.6683i
55.17	−0.711496	−	2.18976i	3.41511	+	2.48122i	2.18331	−	1.58627i	−2.83496	+	2.05972i	3.00344	−	9.24365i	9.41330	−	28.9712i	−19.9287	−	14.4791i	−2.83695	−	8.73123i	6.52734	+	4.74239i
55.18	−0.651503	−	2.00512i	2.48351	+	1.80437i	2.87609	−	2.08960i	10.2088	−	7.41716i	1.99997	−	6.15528i	0.246878	−	0.759812i	−19.7089	−	14.3194i	−5.43142	−	16.7162i	−21.5234	−	15.6377i
55.19	−0.610395	−	1.87860i	−1.44711	−	1.05138i	3.31557	−	2.40890i	5.55274	−	4.03430i	−1.09183	+	3.36030i	−3.59829	+	11.0744i	−19.3335	−	14.0466i	−7.35475	−	22.6356i	−10.9682	−	7.96889i
55.20	−0.560608	−	1.72538i	5.15318	+	3.74400i	3.80950	−	2.76776i	−11.8377	+	8.60063i	3.57090	−	10.9901i	−4.28357	+	13.1835i	−18.6526	−	13.5519i	4.19424	+	12.9085i	21.4757	+	15.6030i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
211.d	even	5	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	211.4.d.a	✓	208
211.d	even	5	1	inner	211.4.d.a	✓	208

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
211.4.d.a	✓	208	1.a	even	1	1	trivial
211.4.d.a	✓	208	211.d	even	5	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(211, [\chi])\).