Newform orbit 197.6.a.b

• Label: 197.6.a.b
• Level: $197$
• Weight: $6$
• Character orbit: 197.a
• Self dual: yes
• Analytic conductor: $31.596$
• Analytic rank: $0$
• Dimension: $43$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$197$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	197.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$31.5956125032$
Analytic rank:	$0$
Dimension:	$43$
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.

$\operatorname{Tr}(f)(q) =$ 43 * q + 12 * q^2 + 98 * q^3 + 752 * q^4 + 146 * q^5 + 144 * q^6 + 831 * q^7 + 699 * q^8 + 3725 * q^9 + 1033 * q^10 + 1370 * q^11 + 3136 * q^12 + 2948 * q^13 + 929 * q^14 + 1859 * q^15 + 14080 * q^16 + 1545 * q^17 + 6757 * q^18 + 12233 * q^19 + 7419 * q^20 + 3674 * q^21 + 10369 * q^22 + 5564 * q^23 + 6813 * q^24 + 35439 * q^25 + 1578 * q^26 + 33755 * q^27 + 38990 * q^28 - 2405 * q^29 + 1483 * q^30 + 31280 * q^31 + 17700 * q^32 + 39326 * q^33 + 9394 * q^34 + 21436 * q^35 + 53290 * q^36 + 35510 * q^37 + 33614 * q^38 + 22963 * q^39 + 50046 * q^40 + 9866 * q^41 + 22195 * q^42 + 51379 * q^43 + 29746 * q^44 + 72219 * q^45 + 35053 * q^46 + 42481 * q^47 + 75938 * q^48 + 175192 * q^49 + 162531 * q^50 + 154051 * q^51 + 210234 * q^52 + 81848 * q^53 + 320743 * q^54 + 105027 * q^55 + 452104 * q^56 + 208589 * q^57 + 159979 * q^58 + 168687 * q^59 + 279933 * q^60 + 148330 * q^61 + 152995 * q^62 + 250849 * q^63 + 540617 * q^64 + 125561 * q^65 + 376032 * q^66 + 395178 * q^67 + 306925 * q^68 + 150249 * q^69 + 271319 * q^70 + 115563 * q^71 + 352975 * q^72 + 247249 * q^73 + 65989 * q^74 + 460002 * q^75 + 440494 * q^76 + 90902 * q^77 + 201225 * q^78 + 222999 * q^79 + 175770 * q^80 + 406335 * q^81 + 172447 * q^82 + 253668 * q^83 - 274214 * q^84 + 114986 * q^85 - 301722 * q^86 + 9553 * q^87 + 79659 * q^88 + 65396 * q^89 - 177829 * q^90 + 360807 * q^91 - 275338 * q^92 - 200055 * q^93 - 249179 * q^94 + 91983 * q^95 - 1089739 * q^96 + 399386 * q^97 - 57978 * q^98 + 119867 * q^99

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	−11.1452			−0.336383			92.2162			−47.6497			3.74907			−75.1526			−671.124			−242.887			531.067
1.2	−10.7119			19.4903			82.7444			86.8228			−208.777			−107.873			−543.567			136.870			−930.035
1.3	−10.2273			19.3367			72.5968			−29.5603			−197.761			191.672			−415.193			130.908			302.320
1.4	−9.97895			−1.74464			67.5794			45.8747			17.4096			1.40539			−355.044			−239.956			−457.781
1.5	−9.66048			−27.2329			61.3248			−56.3745			263.083			56.3197			−283.292			498.631			544.605
1.6	−8.86713			0.0718698			46.6260			8.58831			−0.637279			−242.621			−129.691			−242.995			−76.1537
1.7	−7.81855			−3.85238			29.1298			−63.0871			30.1200			258.975			22.4409			−228.159			493.250
1.8	−6.90647			23.1830			15.6994			95.8550			−160.113			92.5145			112.580			294.453			−662.020
1.9	−6.59656			−22.5190			11.5147			31.9905			148.548			−73.6589			135.133			264.105			−211.027
1.10	−6.46686			10.1034			9.82031			−95.3169			−65.3375			−49.1923			143.433			−140.921			616.401
1.11	−5.80302			12.9092			1.67501			23.4969			−74.9125			−167.264			175.976			−76.3518			−136.353
1.12	−5.60314			−27.4488			−0.604834			60.7084			153.800			236.038			182.689			510.439			−340.158
1.13	−5.44316			28.1713			−2.37201			14.3332			−153.341			119.246			187.092			550.622			−78.0177
1.14	−5.31138			−21.4514			−3.78923			−29.1356			113.937			124.416			190.090			217.164			154.750
1.15	−5.19771			3.76016			−4.98380			5.57792			−19.5442			75.5206			192.231			−228.861			−28.9924
1.16	−4.71670			27.6997			−9.75271			−79.0194			−130.651			189.011			196.935			524.272			372.711
1.17	−3.68168			−9.39506			−18.4452			31.5081			34.5896			14.4366			185.723			−154.733			−116.003
1.18	−1.56744			−0.438374			−29.5431			79.7142			0.687127			218.717			96.4653			−242.808			−124.947
1.19	−0.834938			25.3960			−31.3029			−87.5439			−21.2041			−171.205			52.8540			401.958			73.0938
1.20	−0.742164			−1.92490			−31.4492			−52.2115			1.42859			−106.825			47.0897			−239.295			38.7495

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	197.6.a.b	✓	43

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
197.6.a.b	✓	43	1.a	even	1	1	trivial