Newform orbit 197.14.a.b

• Label: 197.14.a.b
• Level: $197$
• Weight: $14$
• Character orbit: 197.a
• Self dual: yes
• Analytic conductor: $211.245$
• Analytic rank: $0$
• Dimension: $109$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$197$
Weight:	$k$	$=$	$14$
Character orbit:	$[\chi]$	$=$	197.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$211.244930035$
Analytic rank:	$0$
Dimension:	$109$
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.

$\operatorname{Tr}(f)(q) =$ 109 * q + 192 * q^2 + 8018 * q^3 + 471040 * q^4 + 88496 * q^5 + 383232 * q^6 + 1680731 * q^7 + 1820859 * q^8 + 59521391 * q^9 + 16373653 * q^10 + 21199298 * q^11 + 63225856 * q^12 + 59695238 * q^13 + 37888529 * q^14 + 87246239 * q^15 + 2130706432 * q^16 + 228353715 * q^17 + 400647337 * q^18 + 1139301305 * q^19 + 1109969259 * q^20 + 539982398 * q^21 + 1613315649 * q^22 + 920306804 * q^23 + 5542439613 * q^24 + 31241700999 * q^25 + 1864366110 * q^26 + 17825460755 * q^27 + 20413389070 * q^28 + 7185436621 * q^29 + 2050251883 * q^30 + 28475592572 * q^31 + 8334714660 * q^32 + 19623425846 * q^33 + 37845014194 * q^34 + 25255003636 * q^35 + 287968706746 * q^36 + 71523920490 * q^37 + 67778214914 * q^38 + 44951568463 * q^39 + 169184871486 * q^40 + 69139231052 * q^41 + 58715177635 * q^42 + 247544146139 * q^43 + 63861560722 * q^44 + 257443045479 * q^45 + 160530477869 * q^46 + 308496573061 * q^47 + 412228130018 * q^48 + 1736616239908 * q^49 + 1680360028531 * q^50 + 756579032995 * q^51 + 928015404666 * q^52 + 342783723680 * q^53 - 597894730601 * q^54 + 59276330527 * q^55 - 3822929869144 * q^56 - 562905761941 * q^57 + 62740419347 * q^58 + 827401964151 * q^59 - 2247133283907 * q^60 + 988213134514 * q^61 + 1937380192071 * q^62 + 1788190111357 * q^63 + 11682175668457 * q^64 + 2494670804291 * q^65 + 11819807890512 * q^66 + 8038740399790 * q^67 + 10126245189885 * q^68 + 5225665164579 * q^69 + 11464042631319 * q^70 + 4867145119603 * q^71 + 18133468947055 * q^72 + 9684156738615 * q^73 + 16996786880941 * q^74 + 16718732018262 * q^75 + 21454522032798 * q^76 + 6593100920650 * q^77 + 33749579076633 * q^78 + 7591753073823 * q^79 + 24349241260570 * q^80 + 38778649605417 * q^81 + 25555033184251 * q^82 + 16945724819556 * q^83 + 21855489402730 * q^84 + 15544906794766 * q^85 + 18664144286914 * q^86 + 19049540636401 * q^87 + 17318749473003 * q^88 + 11289674998576 * q^89 + 20983303956671 * q^90 + 47242561944227 * q^91 - 25046698097386 * q^92 - 5411884145985 * q^93 + 18338784709341 * q^94 + 6784117894603 * q^95 - 36827486682955 * q^96 + 45969533477736 * q^97 - 42983409526150 * q^98 + 12084396239183 * 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	−179.919			949.600			24179.0			−44809.9			−170851.			555727.			−2.87636e6			−692583.			8.06216e6
1.2	−177.486			−1858.29			23309.4			5365.93			329822.			583422.			−2.68313e6			1.85893e6			−952379.
1.3	−175.365			1521.48			22560.7			48722.0			−266814.			305586.			−2.51977e6			720588.			−8.54411e6
1.4	−173.852			−154.401			22032.6			10183.6			26843.0			−382540.			−2.40622e6			−1.57048e6			−1.77044e6
1.5	−172.035			−63.8588			21404.1			−26311.4			10986.0			−168215.			−2.27295e6			−1.59025e6			4.52650e6
1.6	−168.643			977.710			20248.6			23282.0			−164884.			−126937.			−2.03327e6			−638407.			−3.92635e6
1.7	−161.852			−660.311			18003.9			−63584.1			106872.			71804.7			−1.58807e6			−1.15831e6			1.02912e7
1.8	−160.527			1724.90			17577.0			32215.0			−276893.			−423232.			−1.50655e6			1.38096e6			−5.17138e6
1.9	−158.182			−1675.68			16829.6			7989.80			265063.			−477515.			−1.36632e6			1.21359e6			−1.26384e6
1.10	−155.970			2509.18			16134.6			−12965.5			−391357.			428722.			−1.23881e6			4.70166e6			2.02223e6
1.11	−150.597			−933.812			14487.5			16987.2			140630.			147144.			−948089.			−722318.			−2.55822e6
1.12	−149.393			641.280			14126.2			61634.3			−95802.7			−435746.			−886531.			−1.18308e6			−9.20772e6
1.13	−145.155			−2025.07			12878.0			−10162.8			293949.			345875.			−680200.			2.50658e6			1.47518e6
1.14	−136.248			−2369.27			10371.7			626.226			322809.			−79078.9			−296974.			4.01912e6			−85322.4
1.15	−135.924			−2298.95			10283.3			41046.5			312481.			283206.			−284251.			3.69083e6			−5.57919e6
1.16	−135.355			−1650.52			10129.0			−19198.7			223406.			−557349.			−262189.			1.12989e6			2.59865e6
1.17	−134.862			−985.192			9995.81			−46787.8			132865.			482450.			−243265.			−623719.			6.30990e6
1.18	−133.322			64.3497			9582.75			19563.1			−8579.24			177321.			−185418.			−1.59018e6			−2.60819e6
1.19	−133.256			1856.77			9565.17			−55057.7			−247426.			87617.4			−182983.			1.85327e6			7.33677e6
1.20	−130.527			1003.60			8845.21			−12039.6			−130997.			−78177.1			−85261.9			−587101.			1.57148e6

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	197.14.a.b	✓	109

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
197.14.a.b	✓	109	1.a	even	1	1	trivial