Newform orbit 1859.4.a.l

• Label: 1859.4.a.l
• Level: $1859$
• Weight: $4$
• Character orbit: 1859.a
• Self dual: yes
• Analytic conductor: $109.685$
• Analytic rank: $1$
• Dimension: $36$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$1859 = 11 \cdot 13^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	1859.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$109.684550701$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	no (minimal twist has level 143)
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.

$\operatorname{Tr}(f)(q) =$ 36 * q - 4 * q^2 + 12 * q^3 + 152 * q^4 - 40 * q^5 - 98 * q^6 - 56 * q^7 - 84 * q^8 + 360 * q^9 - 56 * q^10 - 396 * q^11 + 66 * q^12 + 164 * q^14 - 120 * q^15 + 644 * q^16 + 138 * q^17 + 28 * q^18 - 498 * q^19 - 320 * q^20 - 404 * q^21 + 44 * q^22 + 46 * q^23 - 1340 * q^24 + 818 * q^25 + 24 * q^27 - 1382 * q^28 + 262 * q^29 + 104 * q^30 - 660 * q^31 - 106 * q^32 - 132 * q^33 + 640 * q^34 + 68 * q^35 + 1960 * q^36 - 1372 * q^37 + 224 * q^38 + 108 * q^40 - 1216 * q^41 + 82 * q^42 + 436 * q^43 - 1672 * q^44 - 820 * q^45 - 2512 * q^46 + 140 * q^47 - 1944 * q^48 + 1192 * q^49 - 3484 * q^50 + 712 * q^51 + 146 * q^53 - 3078 * q^54 + 440 * q^55 - 102 * q^56 - 3656 * q^57 + 324 * q^58 - 404 * q^59 + 2944 * q^60 - 590 * q^61 + 1776 * q^62 - 4364 * q^63 + 2514 * q^64 + 1078 * q^66 - 2236 * q^67 - 1530 * q^68 + 12 * q^69 - 4852 * q^70 - 292 * q^71 - 2990 * q^72 - 1936 * q^73 + 1568 * q^74 + 4688 * q^75 - 7398 * q^76 + 616 * q^77 - 1464 * q^79 + 808 * q^80 + 3780 * q^81 - 4072 * q^82 - 4422 * q^83 + 2678 * q^84 - 3700 * q^85 + 2588 * q^86 - 1832 * q^87 + 924 * q^88 - 6856 * q^89 - 3422 * q^90 - 668 * q^92 - 840 * q^93 - 4166 * q^94 - 256 * q^95 - 18290 * q^96 - 2776 * q^97 - 4608 * q^98 - 3960 * 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	−5.40970			9.04984			21.2648			14.9789			−48.9569			−21.1440			−71.7586			54.8996			−81.0315
1.2	−5.37051			6.42352			20.8423			−1.04643			−34.4976			−14.1100			−68.9699			14.2616			5.61984
1.3	−5.31556			−6.97612			20.2552			−11.0780			37.0820			−15.5383			−65.1431			21.6662			58.8858
1.4	−4.91072			4.96902			16.1152			−14.5097			−24.4015			24.8330			−39.8514			−2.30886			71.2531
1.5	−4.68862			−2.64231			13.9831			−16.8988			12.3888			−13.2904			−28.0526			−20.0182			79.2322
1.6	−4.48294			−3.05507			12.0967			15.8460			13.6957			14.1972			−18.3654			−17.6666			−71.0368
1.7	−3.97184			1.90642			7.77550			18.9601			−7.57198			23.8934			0.891668			−23.3656			−75.3066
1.8	−3.52500			6.60993			4.42564			−15.7848			−23.3000			−35.5340			12.5996			16.6911			55.6415
1.9	−3.45591			−5.41746			3.94332			9.57590			18.7223			−27.8655			14.0195			2.34888			−33.0934
1.10	−3.25823			−8.58536			2.61606			2.74949			27.9731			−10.9805			17.5421			46.7084			−8.95848
1.11	−3.04437			6.04232			1.26822			6.26745			−18.3951			22.1223			20.4941			9.50964			−19.0805
1.12	−2.93776			9.49640			0.630432			−20.5709			−27.8981			−4.19587			21.6500			63.1815			60.4323
1.13	−2.56135			−1.18355			−1.43947			−4.85042			3.03148			6.35045			24.1778			−25.5992			12.4237
1.14	−1.74560			−4.37143			−4.95287			−9.81487			7.63078			18.0536			22.6106			−7.89058			17.1329
1.15	−1.63327			3.36108			−5.33243			4.44226			−5.48955			−30.4921			21.7754			−15.7031			−7.25541
1.16	−0.851378			5.53627			−7.27515			7.50257			−4.71346			8.31728			13.0049			3.65026			−6.38753
1.17	−0.236535			−7.74253			−7.94405			11.7890			1.83138			5.71517			3.77132			32.9468			−2.78850
1.18	0.231915			8.68804			−7.94622			−0.297636			2.01489			−7.88297			−3.69817			48.4820			−0.0690264
1.19	0.665052			−3.21477			−7.55771			−10.5229			−2.13799			−28.9946			−10.3467			−16.6653			−6.99830
1.20	0.677132			5.62189			−7.54149			21.4343			3.80677			−10.4645			−10.5236			4.60569			14.5139

Atkin-Lehner signs

$p$	Sign
$11$	$+1$
$13$	$-1$

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	1859.4.a.l		36
13.b	even	2	1		1859.4.a.m		36
13.f	odd	12	2		143.4.j.a	✓	72

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
143.4.j.a	✓	72	13.f	odd	12	2
1859.4.a.l		36	1.a	even	1	1	trivial
1859.4.a.m		36	13.b	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^36 + 4*T2^35 - 212*T2^34 - 820*T2^33 + 20423*T2^32 + 75918*T2^31 - 1184783*T2^30 - 4200200*T2^29 + 46244111*T2^28 + 154821080*T2^27 - 1285326700*T2^26 - 4012149440*T2^25 + 26264677854*T2^24 + 75151637812*T2^23 - 401699472382*T2^22 - 1029478839272*T2^21 + 4637723548279*T2^20 + 10307031002940*T2^19 - 40464222506748*T2^18 - 74431568823068*T2^17 + 265208384337747*T2^16 + 376188613475118*T2^15 - 1286848715373787*T2^14 - 1251303882503856*T2^13 + 4499760894697089*T2^12 + 2355774337541752*T2^11 - 10812220677044764*T2^10 - 1080114073257296*T2^9 + 16376956365936896*T2^8 - 4543874183105664*T2^7 - 13121870364504512*T2^6 + 8143987953568768*T2^5 + 3212080510775296*T2^4 - 3813314312159232*T2^3 + 634603331321856*T2^2 + 189549790101504*T2 - 43206514311168