Newform orbit 276.3.f.b

• Label: 276.3.f.b
• Level: $276$
• Weight: $3$
• Character orbit: 276.f
• Analytic conductor: $7.520$
• Analytic rank: $0$
• Dimension: $40$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	276.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.52045529634\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 40 q + 4 q^{2} + 8 q^{4} + 4 q^{5} - 12 q^{6} - 44 q^{8} - 120 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
139.1	−1.99846	−	0.0784910i		−	1.73205i	3.98768	+	0.313722i	−0.934476			−0.135950	+	3.46143i		−	12.0780i	−7.94459	−	0.939958i	−3.00000			1.86751	+	0.0733480i
139.2	−1.99846	+	0.0784910i			1.73205i	3.98768	−	0.313722i	−0.934476			−0.135950	−	3.46143i			12.0780i	−7.94459	+	0.939958i	−3.00000			1.86751	−	0.0733480i
139.3	−1.92697	−	0.535525i		−	1.73205i	3.42643	+	2.06388i	−6.57597			−0.927557	+	3.33761i			5.60382i	−5.49736	−	5.81198i	−3.00000			12.6717	+	3.52160i
139.4	−1.92697	+	0.535525i			1.73205i	3.42643	−	2.06388i	−6.57597			−0.927557	−	3.33761i		−	5.60382i	−5.49736	+	5.81198i	−3.00000			12.6717	−	3.52160i
139.5	−1.87686	−	0.690935i			1.73205i	3.04522	+	2.59358i	−1.28200			1.19673	−	3.25082i			2.36368i	−3.92345	−	6.97184i	−3.00000			2.40614	+	0.885782i
139.6	−1.87686	+	0.690935i		−	1.73205i	3.04522	−	2.59358i	−1.28200			1.19673	+	3.25082i		−	2.36368i	−3.92345	+	6.97184i	−3.00000			2.40614	−	0.885782i
139.7	−1.77812	−	0.915580i			1.73205i	2.32343	+	3.25602i	5.27503			1.58583	−	3.07980i		−	6.54978i	−1.15018	−	7.91689i	−3.00000			−9.37964	−	4.82972i
139.8	−1.77812	+	0.915580i		−	1.73205i	2.32343	−	3.25602i	5.27503			1.58583	+	3.07980i			6.54978i	−1.15018	+	7.91689i	−3.00000			−9.37964	+	4.82972i
139.9	−1.70309	−	1.04857i		−	1.73205i	1.80101	+	3.57161i	9.44418			−1.81617	+	2.94983i		−	6.03937i	0.677795	−	7.97124i	−3.00000			−16.0843	−	9.90287i
139.10	−1.70309	+	1.04857i			1.73205i	1.80101	−	3.57161i	9.44418			−1.81617	−	2.94983i			6.03937i	0.677795	+	7.97124i	−3.00000			−16.0843	+	9.90287i
139.11	−1.51663	−	1.30378i		−	1.73205i	0.600313	+	3.95470i	−0.0471222			−2.25821	+	2.62687i			2.88805i	4.24561	−	6.78047i	−3.00000			0.0714667	+	0.0614370i
139.12	−1.51663	+	1.30378i			1.73205i	0.600313	−	3.95470i	−0.0471222			−2.25821	−	2.62687i		−	2.88805i	4.24561	+	6.78047i	−3.00000			0.0714667	−	0.0614370i
139.13	−0.678740	−	1.88131i		−	1.73205i	−3.07862	+	2.55384i	4.99031			−3.25852	+	1.17561i			2.08864i	6.89413	+	4.05844i	−3.00000			−3.38713	−	9.38830i
139.14	−0.678740	+	1.88131i			1.73205i	−3.07862	−	2.55384i	4.99031			−3.25852	−	1.17561i		−	2.08864i	6.89413	−	4.05844i	−3.00000			−3.38713	+	9.38830i
139.15	−0.431523	−	1.95289i		−	1.73205i	−3.62758	+	1.68544i	−9.02044			−3.38251	+	0.747419i		−	1.43355i	4.85685	+	6.35696i	−3.00000			3.89253	+	17.6159i
139.16	−0.431523	+	1.95289i			1.73205i	−3.62758	−	1.68544i	−9.02044			−3.38251	−	0.747419i			1.43355i	4.85685	−	6.35696i	−3.00000			3.89253	−	17.6159i
139.17	−0.0758829	−	1.99856i		−	1.73205i	−3.98848	+	0.303313i	1.44548			−3.46161	+	0.131433i			10.3854i	0.908847	+	7.94821i	−3.00000			−0.109688	−	2.88889i
139.18	−0.0758829	+	1.99856i			1.73205i	−3.98848	−	0.303313i	1.44548			−3.46161	−	0.131433i		−	10.3854i	0.908847	−	7.94821i	−3.00000			−0.109688	+	2.88889i
139.19	0.268173	−	1.98194i			1.73205i	−3.85617	−	1.06301i	−0.0477853			3.43282	+	0.464490i		−	3.46303i	−3.14094	+	7.35762i	−3.00000			−0.0128147	+	0.0947075i
139.20	0.268173	+	1.98194i		−	1.73205i	−3.85617	+	1.06301i	−0.0477853			3.43282	−	0.464490i			3.46303i	−3.14094	−	7.35762i	−3.00000			−0.0128147	−	0.0947075i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	276.3.f.b	✓	40
4.b	odd	2	1	inner	276.3.f.b	✓	40

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
276.3.f.b	✓	40	1.a	even	1	1	trivial
276.3.f.b	✓	40	4.b	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^20 - 2*T5^19 - 284*T5^18 + 592*T5^17 + 32244*T5^16 - 71352*T5^15 - 1880752*T5^14 + 4459360*T5^13 + 60003280*T5^12 - 152891808*T5^11 - 1016897664*T5^10 + 2773111296*T5^9 + 7875507968*T5^8 - 22658983936*T5^7 - 16501066752*T5^6 + 46351665152*T5^5 + 13172981760*T5^4 - 24869715968*T5^3 - 3709714432*T5^2 - 179634176*T5 - 2883584