Newform orbit 155.3.g.a

• Label: 155.3.g.a
• Level: $155$
• Weight: $3$
• Character orbit: 155.g
• Analytic conductor: $4.223$
• Analytic rank: $0$
• Dimension: $60$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 155 = 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	155.g (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.22344409758\)
Analytic rank:	\(0\)
Dimension:	\(60\)
Relative dimension:	\(30\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 60 q - 4 q^{2} - 4 q^{5} + 16 q^{6} + 12 q^{7} + 18 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
32.1	−2.75675	−	2.75675i	3.21788	−	3.21788i			11.1994i	−0.999325	+	4.89912i	−17.7418			7.38673	+	7.38673i	19.8469	−	19.8469i		−	11.7095i	16.2605	−	10.7508i
32.2	−2.59879	−	2.59879i	−1.97722	+	1.97722i			9.50738i	3.82801	+	3.21658i	10.2768			−4.39840	−	4.39840i	14.3125	−	14.3125i			1.18119i	−1.58898	−	18.3074i
32.3	−2.50922	−	2.50922i	−0.165057	+	0.165057i			8.59237i	−4.70969	−	1.67894i	0.828330			−7.88728	−	7.88728i	11.5233	−	11.5233i			8.94551i	7.60480	+	16.0305i
32.4	−2.31360	−	2.31360i	−3.59020	+	3.59020i			6.70551i	−4.95049	+	0.701893i	16.6126			8.15587	+	8.15587i	6.25946	−	6.25946i		−	16.7791i	13.0774	+	9.82956i
32.5	−2.26298	−	2.26298i	−0.597152	+	0.597152i			6.24219i	1.47553	−	4.77732i	2.70269			5.70620	+	5.70620i	5.07405	−	5.07405i			8.28682i	−14.1501	+	7.47190i
32.6	−1.92359	−	1.92359i	3.08167	−	3.08167i			3.40043i	−2.81940	−	4.12928i	−11.8557			0.415517	+	0.415517i	−1.15334	+	1.15334i		−	9.99333i	−2.51967	+	13.3664i
32.7	−1.76338	−	1.76338i	3.27594	−	3.27594i			2.21903i	4.96270	+	0.609590i	−11.5535			−7.12415	−	7.12415i	−3.14054	+	3.14054i		−	12.4636i	−7.67619	−	9.82607i
32.8	−1.59662	−	1.59662i	1.03084	−	1.03084i			1.09836i	−2.97271	+	4.02032i	−3.29170			−1.26156	−	1.26156i	−4.63280	+	4.63280i			6.87476i	11.1652	−	1.67264i
32.9	−1.57013	−	1.57013i	−3.13568	+	3.13568i			0.930593i	3.44735	−	3.62157i	9.84684			−2.36103	−	2.36103i	−4.81936	+	4.81936i		−	10.6650i	−11.0991	+	0.273537i
32.10	−1.53139	−	1.53139i	0.237637	−	0.237637i			0.690305i	3.90424	+	3.12360i	−0.727830			4.56842	+	4.56842i	−5.06843	+	5.06843i			8.88706i	−1.19546	−	10.7624i
32.11	−1.14704	−	1.14704i	−3.24759	+	3.24759i		−	1.36859i	−1.26379	+	4.83765i	7.45024			−5.34946	−	5.34946i	−6.15800	+	6.15800i		−	12.0936i	6.99861	−	4.09936i
32.12	−0.687549	−	0.687549i	−0.680934	+	0.680934i		−	3.05455i	−2.98425	−	4.01177i	0.936352			−0.993116	−	0.993116i	−4.85035	+	4.85035i			8.07266i	−0.706471	+	4.81010i
32.13	−0.377855	−	0.377855i	−1.30627	+	1.30627i		−	3.71445i	−4.97815	+	0.466876i	0.987160			7.80803	+	7.80803i	−2.91494	+	2.91494i			5.58732i	2.05743	+	1.70461i
32.14	−0.317503	−	0.317503i	2.94287	−	2.94287i		−	3.79838i	2.80922	−	4.13622i	−1.86874			7.48028	+	7.48028i	−2.47601	+	2.47601i		−	8.32102i	−2.20520	+	0.421327i
32.15	−0.236719	−	0.236719i	0.261745	−	0.261745i		−	3.88793i	4.19510	−	2.72050i	−0.123920			−7.03777	−	7.03777i	−1.86722	+	1.86722i			8.86298i	−1.63705	−	0.349066i
32.16	−0.146842	−	0.146842i	3.25722	−	3.25722i		−	3.95687i	−4.60112	+	1.95695i	−0.956596			−3.91523	−	3.91523i	−1.16841	+	1.16841i		−	12.2189i	0.963004	+	0.388276i
32.17	0.107744	+	0.107744i	−2.89031	+	2.89031i		−	3.97678i	2.06237	+	4.55485i	−0.622826			3.24400	+	3.24400i	0.859448	−	0.859448i		−	7.70781i	−0.268549	+	0.712963i
32.18	0.405879	+	0.405879i	2.41474	−	2.41474i		−	3.67052i	2.13184	+	4.52275i	1.96018			3.72593	+	3.72593i	3.11331	−	3.11331i		−	2.66189i	−0.970419	+	2.70096i
32.19	0.733888	+	0.733888i	−3.80636	+	3.80636i		−	2.92282i	−1.08157	−	4.88162i	−5.58688			1.17736	+	1.17736i	5.08057	−	5.08057i		−	19.9767i	2.78880	−	4.37631i
32.20	0.895982	+	0.895982i	−1.37235	+	1.37235i		−	2.39443i	4.99812	+	0.136986i	−2.45921			−0.785898	−	0.785898i	5.72930	−	5.72930i			5.23330i	4.35549	+	4.60097i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	155.3.g.a	✓	60
5.c	odd	4	1	inner	155.3.g.a	✓	60

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
155.3.g.a	✓	60	1.a	even	1	1	trivial
155.3.g.a	✓	60	5.c	odd	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(155, [\chi])\).