Newform orbit 197.4.a.a

• Label: 197.4.a.a
• Level: $197$
• Weight: $4$
• Character orbit: 197.a
• Self dual: yes
• Analytic conductor: $11.623$
• Analytic rank: $1$
• Dimension: $22$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	197.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(11.6233762711\)
Analytic rank:	\(1\)
Dimension:	\(22\)
Twist minimal:	yes
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 22 q - 6 q^{2} - 34 q^{3} + 68 q^{4} - 31 q^{5} - 24 q^{6} - 102 q^{7} - 93 q^{8} + 152 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1.1	−5.55450			−7.58749			22.8525			−2.05060			42.1447			−31.5579			−82.4982			30.5700			11.3901
1.2	−5.05368			2.19389			17.5397			16.4586			−11.0872			−13.1699			−48.2106			−22.1869			−83.1765
1.3	−4.89168			1.98437			15.9285			3.25325			−9.70688			−2.13592			−38.7836			−23.0623			−15.9139
1.4	−3.99259			7.91622			7.94077			−8.81975			−31.6062			2.31327			0.236468			35.6665			35.2137
1.5	−3.51341			−5.88377			4.34403			−3.63670			20.6721			−4.62984			12.8449			7.61880			12.7772
1.6	−3.25705			−0.297531			2.60839			−8.26136			0.969073			15.5528			17.5608			−26.9115			26.9077
1.7	−3.10465			−9.85776			1.63883			−19.1154			30.6049			8.54659			19.7492			70.1754			59.3466
1.8	−1.77551			7.37778			−4.84756			−10.0693			−13.0993			−1.88753			22.8110			27.4316			17.8781
1.9	−1.76902			2.15212			−4.87057			12.0580			−3.80715			−14.2747			22.7683			−22.3684			−21.3308
1.10	−1.44472			−9.83891			−5.91279			14.8390			14.2144			−21.5448			20.1001			69.8042			−21.4381
1.11	−0.906472			−8.01793			−7.17831			3.79100			7.26803			26.0997			13.7587			37.2872			−3.43644
1.12	−0.567396			−4.62395			−7.67806			2.48244			2.62361			27.3890			8.89567			−5.61907			−1.40853
1.13	0.887037			2.87223			−7.21316			−0.0802046			2.54777			9.14732			−13.4946			−18.7503			−0.0711445
1.14	1.28043			5.48907			−6.36049			3.36905			7.02839			−33.5513			−18.3876			3.12992			4.31384
1.15	2.32035			6.85995			−2.61598			−20.6548			15.9175			−15.9478			−24.6328			20.0590			−47.9264
1.16	2.44630			−3.77168			−2.01559			19.5805			−9.22669			−29.7228			−24.5012			−12.7744			47.8998
1.17	2.52805			−1.15089			−1.60896			−0.582279			−2.90951			11.2805			−24.2919			−25.6755			−1.47203
1.18	3.21645			1.35507			2.34554			−13.0467			4.35850			1.96440			−18.1873			−25.1638			−41.9641
1.19	3.48860			−8.28964			4.17032			8.64850			−28.9192			6.87715			−13.3602			41.7181			30.1711
1.20	4.11340			−2.85529			8.92002			−0.445853			−11.7449			−30.9976			3.78443			−18.8473			−1.83397

Atkin-Lehner signs

\( p \)	Sign
\(197\)	\( -1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	197.4.a.a	✓	22
3.b	odd	2	1		1773.4.a.c		22

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
197.4.a.a	✓	22	1.a	even	1	1	trivial
1773.4.a.c		22	3.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^22 + 6*T2^21 - 104*T2^20 - 633*T2^19 + 4538*T2^18 + 28116*T2^17 - 108605*T2^16 - 689191*T2^15 + 1558247*T2^14 + 10258748*T2^13 - 13661770*T2^12 - 96064303*T2^11 + 70035192*T2^10 + 566459140*T2^9 - 172140509*T2^8 - 2042979529*T2^7 - 30070986*T2^6 + 4205220422*T2^5 + 1063464332*T2^4 - 4272899272*T2^3 - 1741705168*T2^2 + 1565378304*T2 + 772688448