Newform orbit 220.2.o.a

• Label: 220.2.o.a
• Level: $220$
• Weight: $2$
• Character orbit: 220.o
• Analytic conductor: $1.757$
• Analytic rank: $0$
• Dimension: $128$
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.o (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.75670884447\)
Analytic rank:	\(0\)
Dimension:	\(128\)
Relative dimension:	\(32\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 128 q - 6 q^{4} - 6 q^{5} - 10 q^{6} - 36 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
19.1	−1.40908	−	0.120420i	0.358574	+	1.10358i	1.97100	+	0.339361i	2.17434	+	0.521772i	−0.372366	−	1.59820i	1.17526	+	0.381865i	−2.73642	−	0.715533i	1.33774	−	0.971928i	−3.00098	−	0.997050i
19.2	−1.39601	+	0.226162i	0.0565130	+	0.173929i	1.89770	−	0.631450i	−2.21829	−	0.281383i	−0.118229	−	0.230026i	1.67119	+	0.543002i	−2.50641	+	1.31070i	2.39999	−	1.74370i	3.16040	−	0.108880i
19.3	−1.30312	−	0.549445i	−0.792163	−	2.43803i	1.39622	+	1.43198i	−2.17036	−	0.538101i	−0.307283	+	3.61228i	−0.0886239	−	0.0287956i	−1.03264	−	2.63318i	−2.88940	+	2.09927i	2.53257	+	1.89370i
19.4	−1.26045	+	0.641292i	−0.873724	−	2.68904i	1.17749	−	1.61664i	0.802730	+	2.08701i	2.82575	+	2.82911i	3.45331	+	1.12205i	−0.447436	+	2.79281i	−4.04052	+	2.93561i	−2.35019	−	2.11580i
19.5	−1.23145	−	0.695360i	0.956633	+	2.94421i	1.03295	+	1.71261i	−1.38646	+	1.75435i	0.869240	−	4.29086i	1.89963	+	0.617228i	−0.0811505	−	2.82726i	−5.32619	+	3.86970i	2.92726	−	1.19630i
19.6	−1.21462	+	0.724368i	−0.584931	−	1.80023i	0.950583	−	1.75966i	0.815527	−	2.08205i	2.01450	+	1.76289i	−2.76001	−	0.896781i	0.120044	+	2.82588i	−0.471640	+	0.342666i	0.517615	+	3.11963i
19.7	−1.20080	−	0.747052i	0.370610	+	1.14062i	0.883825	+	1.79412i	0.123712	−	2.23264i	0.407076	−	1.64652i	−4.41757	−	1.43535i	0.279004	−	2.81463i	1.26339	−	0.917906i	−1.81645	+	2.58853i
19.8	−1.06425	+	0.931326i	0.584931	+	1.80023i	0.265262	−	1.98233i	0.815527	−	2.08205i	−2.29912	−	1.37114i	2.76001	+	0.896781i	1.56389	+	2.35674i	−0.471640	+	0.342666i	1.07114	+	2.97534i
19.9	−0.999406	+	1.00059i	0.873724	+	2.68904i	−0.00237383	−	2.00000i	0.802730	+	2.08701i	−3.56384	−	1.81321i	−3.45331	−	1.12205i	2.00356	+	1.99644i	−4.04052	+	2.93561i	−2.89050	−	1.28257i
19.10	−0.914274	−	1.07894i	−0.319262	−	0.982588i	−0.328205	+	1.97289i	−0.199146	+	2.22718i	−0.768256	+	1.24282i	1.25217	+	0.406854i	2.42869	−	1.44965i	1.56350	−	1.13595i	2.58506	−	1.82139i
19.11	−0.743603	−	1.20294i	−0.319262	−	0.982588i	−0.894110	+	1.78901i	2.05664	−	0.877637i	−0.944586	+	1.11471i	1.25217	+	0.406854i	2.81693	−	0.254757i	1.56350	−	1.13595i	−2.58506	−	1.82139i
19.12	−0.646484	+	1.25780i	−0.0565130	−	0.173929i	−1.16412	−	1.62629i	−2.21829	−	0.281383i	0.255303	+	0.0413605i	−1.67119	−	0.543002i	2.79813	−	0.412850i	2.39999	−	1.74370i	1.78801	−	2.60826i
19.13	−0.339423	−	1.37288i	0.370610	+	1.14062i	−1.76958	+	0.931971i	−2.08514	+	0.807582i	1.44014	−	0.895954i	−4.41757	−	1.43535i	1.88012	+	2.11309i	1.26339	−	0.917906i	1.81645	+	2.58853i
19.14	−0.320903	+	1.37732i	−0.358574	−	1.10358i	−1.79404	−	0.883975i	2.17434	+	0.521772i	1.63505	−	0.139731i	−1.17526	−	0.381865i	1.79323	−	2.18731i	1.33774	−	0.971928i	−1.41640	+	2.82733i
19.15	−0.280787	−	1.38606i	0.956633	+	2.94421i	−1.84232	+	0.778374i	1.24004	−	1.86072i	3.81224	−	2.15265i	1.89963	+	0.617228i	1.59617	+	2.33500i	−5.32619	+	3.86970i	−2.92726	−	1.19630i
19.16	−0.119869	−	1.40912i	−0.792163	−	2.43803i	−1.97126	+	0.337820i	−1.18244	−	1.89785i	−3.34053	+	1.40850i	−0.0886239	−	0.0287956i	0.712323	+	2.73726i	−2.88940	+	2.09927i	−2.53257	+	1.89370i
19.17	0.119869	+	1.40912i	0.792163	+	2.43803i	−1.97126	+	0.337820i	−2.17036	−	0.538101i	−3.34053	+	1.40850i	0.0886239	+	0.0287956i	−0.712323	−	2.73726i	−2.88940	+	2.09927i	0.498094	−	3.12280i
19.18	0.280787	+	1.38606i	−0.956633	−	2.94421i	−1.84232	+	0.778374i	−1.38646	+	1.75435i	3.81224	−	2.15265i	−1.89963	−	0.617228i	−1.59617	−	2.33500i	−5.32619	+	3.86970i	−2.82093	−	1.42912i
19.19	0.320903	−	1.37732i	0.358574	+	1.10358i	−1.79404	−	0.883975i	1.16814	+	1.90668i	1.63505	−	0.139731i	1.17526	+	0.381865i	−1.79323	+	2.18731i	1.33774	−	0.971928i	3.00098	−	0.997050i
19.20	0.339423	+	1.37288i	−0.370610	−	1.14062i	−1.76958	+	0.931971i	0.123712	−	2.23264i	1.44014	−	0.895954i	4.41757	+	1.43535i	−1.88012	−	2.11309i	1.26339	−	0.917906i	3.10714	−	0.587967i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
5.b	even	2	1	inner
11.d	odd	10	1	inner
20.d	odd	2	1	inner
44.g	even	10	1	inner
55.h	odd	10	1	inner
220.o	even	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	220.2.o.a	✓	128
4.b	odd	2	1	inner	220.2.o.a	✓	128
5.b	even	2	1	inner	220.2.o.a	✓	128
11.d	odd	10	1	inner	220.2.o.a	✓	128
20.d	odd	2	1	inner	220.2.o.a	✓	128
44.g	even	10	1	inner	220.2.o.a	✓	128
55.h	odd	10	1	inner	220.2.o.a	✓	128
220.o	even	10	1	inner	220.2.o.a	✓	128

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
220.2.o.a	✓	128	1.a	even	1	1	trivial
220.2.o.a	✓	128	4.b	odd	2	1	inner
220.2.o.a	✓	128	5.b	even	2	1	inner
220.2.o.a	✓	128	11.d	odd	10	1	inner
220.2.o.a	✓	128	20.d	odd	2	1	inner
220.2.o.a	✓	128	44.g	even	10	1	inner
220.2.o.a	✓	128	55.h	odd	10	1	inner
220.2.o.a	✓	128	220.o	even	10	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(220, [\chi])\).