Newform orbit 62.7.f.a

• Label: 62.7.f.a
• Level: $62$
• Weight: $7$
• Character orbit: 62.f
• Analytic conductor: $14.263$
• Analytic rank: $0$
• Dimension: $64$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	62.f (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.2633531844\)
Analytic rank:	\(0\)
Dimension:	\(64\)
Relative dimension:	\(16\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 64 q - 512 q^{4} - 288 q^{5} - 692 q^{7} + 3248 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
15.1	−4.57649	+	3.32502i	−25.5799	+	35.2077i	9.88854	−	30.4338i	−242.487				−	246.181i	114.010	−	350.886i	55.9381	+	172.160i	−359.977	−	1107.90i	1109.74	−	806.272i
15.2	−4.57649	+	3.32502i	−16.9719	+	23.3599i	9.88854	−	30.4338i	12.8309				−	163.338i	−163.532	+	503.299i	55.9381	+	172.160i	−32.3638	−	99.6054i	−58.7205	+	42.6630i
15.3	−4.57649	+	3.32502i	−12.3480	+	16.9955i	9.88854	−	30.4338i	59.5260				−	118.837i	−30.1125	+	92.6767i	55.9381	+	172.160i	88.8978	+	273.599i	−272.420	+	197.925i
15.4	−4.57649	+	3.32502i	1.22115	−	1.68076i	9.88854	−	30.4338i	−33.3114					11.7523i	91.0827	−	280.324i	55.9381	+	172.160i	223.940	+	689.215i	152.449	−	110.761i
15.5	−4.57649	+	3.32502i	8.28172	−	11.3988i	9.88854	−	30.4338i	−177.402					79.7034i	−37.1950	+	114.474i	55.9381	+	172.160i	163.927	+	504.517i	811.879	−	589.865i
15.6	−4.57649	+	3.32502i	12.2169	−	16.8151i	9.88854	−	30.4338i	201.726					117.576i	109.915	−	338.284i	55.9381	+	172.160i	91.7775	+	282.462i	−923.196	+	670.741i
15.7	−4.57649	+	3.32502i	20.4297	−	28.1190i	9.88854	−	30.4338i	128.397					196.615i	−202.944	+	624.597i	55.9381	+	172.160i	−148.035	−	455.605i	−587.607	+	426.921i
15.8	−4.57649	+	3.32502i	30.6389	−	42.1708i	9.88854	−	30.4338i	−102.487					294.869i	114.954	−	353.792i	55.9381	+	172.160i	−614.363	−	1890.82i	469.030	−	340.771i
15.9	4.57649	−	3.32502i	−24.4446	+	33.6452i	9.88854	−	30.4338i	110.694					235.256i	−126.529	+	389.418i	−55.9381	−	172.160i	−309.183	−	951.568i	506.591	−	368.060i
15.10	4.57649	−	3.32502i	−22.4820	+	30.9438i	9.88854	−	30.4338i	−120.991					216.367i	61.2460	−	188.496i	−55.9381	−	172.160i	−226.806	−	698.038i	−553.716	+	402.298i
15.11	4.57649	−	3.32502i	−3.06561	+	4.21946i	9.88854	−	30.4338i	−100.632					29.5035i	61.2265	−	188.436i	−55.9381	−	172.160i	216.868	+	667.450i	−460.541	+	334.602i
15.12	4.57649	−	3.32502i	−3.00199	+	4.13188i	9.88854	−	30.4338i	176.963					28.8912i	7.81304	−	24.0461i	−55.9381	−	172.160i	217.213	+	668.512i	809.870	−	588.405i
15.13	4.57649	−	3.32502i	0.519266	−	0.714708i	9.88854	−	30.4338i	−131.510				−	4.99742i	−80.4012	+	247.449i	−55.9381	−	172.160i	225.032	+	692.578i	−601.854	+	437.272i
15.14	4.57649	−	3.32502i	15.4410	−	21.2527i	9.88854	−	30.4338i	6.26454				−	148.604i	109.443	−	336.831i	−55.9381	−	172.160i	12.0203	+	36.9947i	28.6696	−	20.8297i
15.15	4.57649	−	3.32502i	24.8780	−	34.2416i	9.88854	−	30.4338i	150.694				−	239.426i	33.3766	−	102.723i	−55.9381	−	172.160i	−328.299	−	1010.40i	689.650	−	501.060i
15.16	4.57649	−	3.32502i	30.0446	−	41.3528i	9.88854	−	30.4338i	−171.272				−	289.150i	−121.313	+	373.364i	−55.9381	−	172.160i	−582.105	−	1791.54i	−783.825	+	569.482i
23.1	−1.74806	+	5.37999i	−43.6742	+	14.1906i	−25.8885	−	18.8091i	144.799				−	259.773i	285.748	+	207.608i	146.448	−	106.400i	1116.29	−	811.032i	−253.118	+	779.019i
23.2	−1.74806	+	5.37999i	−35.2660	+	11.4586i	−25.8885	−	18.8091i	−54.3091				−	209.761i	−333.682	−	242.434i	146.448	−	106.400i	522.615	−	379.702i	94.9357	−	292.182i
23.3	−1.74806	+	5.37999i	−12.9095	+	4.19455i	−25.8885	−	18.8091i	−246.570				−	76.7853i	34.8772	+	25.3397i	146.448	−	106.400i	−440.712	+	320.196i	431.020	−	1326.54i
23.4	−1.74806	+	5.37999i	−5.83008	+	1.89431i	−25.8885	−	18.8091i	226.620				−	34.6772i	−495.718	−	360.160i	146.448	−	106.400i	−559.372	+	406.407i	−396.147	+	1219.21i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
31.f	odd	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	62.7.f.a	✓	64
31.f	odd	10	1	inner	62.7.f.a	✓	64

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
62.7.f.a	✓	64	1.a	even	1	1	trivial
62.7.f.a	✓	64	31.f	odd	10	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{7}^{\mathrm{new}}(62, [\chi])\).