Newform orbit 1859.4.a.o

• Label: 1859.4.a.o
• Level: $1859$
• Weight: $4$
• Character orbit: 1859.a
• Self dual: yes
• Analytic conductor: $109.685$
• Analytic rank: $1$
• Dimension: $39$
• 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:	$39$
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.

$\operatorname{Tr}(f)(q) =$ 39 * q - 23 * q^3 + 114 * q^4 + 23 * q^5 + 77 * q^6 - 4 * q^7 - 21 * q^8 + 260 * q^9 - 158 * q^10 - 429 * q^11 - 351 * q^12 - 176 * q^14 + 30 * q^15 + 230 * q^16 - 244 * q^17 + 21 * q^18 - 70 * q^19 + 366 * q^20 - 142 * q^21 - 47 * q^23 + 846 * q^24 + 322 * q^25 - 416 * q^27 + 1131 * q^28 - 838 * q^29 - 293 * q^30 + 507 * q^31 - 1433 * q^32 + 253 * q^33 + 166 * q^34 - 498 * q^35 + 815 * q^36 + 89 * q^37 + 81 * q^38 - 2917 * q^40 + 618 * q^41 - 318 * q^42 - 1064 * q^43 - 1254 * q^44 + 238 * q^45 - 1331 * q^46 + 1499 * q^47 - 1460 * q^48 - 413 * q^49 - 2459 * q^50 - 2350 * q^51 - 2745 * q^53 - 845 * q^54 - 253 * q^55 - 2904 * q^56 + 1450 * q^57 - 2509 * q^58 + 2285 * q^59 - 3566 * q^60 - 6218 * q^61 - 911 * q^62 - 1930 * q^63 + 67 * q^64 - 847 * q^66 + 546 * q^67 - 170 * q^68 - 5254 * q^69 - 2195 * q^70 - 263 * q^71 - 2393 * q^72 - 1148 * q^73 + 775 * q^74 - 5385 * q^75 - 7247 * q^76 + 44 * q^77 - 3666 * q^79 + 5594 * q^80 - 1901 * q^81 - 4414 * q^82 + 2722 * q^83 - 9971 * q^84 + 1858 * q^85 + 2478 * q^86 - 2284 * q^87 + 231 * q^88 + 13 * q^89 - 6771 * q^90 - 2232 * q^92 - 1082 * q^93 - 7330 * q^94 - 2352 * q^95 + 5770 * q^96 - 1197 * q^97 + 6813 * q^98 - 2860 * 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	−5.49304			−8.44279			22.1734			19.5698			46.3765			18.0683			−77.8552			44.2807			−107.497
1.2	−5.13075			4.07791			18.3246			9.39838			−20.9227			18.3779			−52.9729			−10.3707			−48.2207
1.3	−5.06016			−3.81429			17.6052			13.6056			19.3009			−15.5193			−48.6040			−12.4512			−68.8465
1.4	−4.86773			−7.77085			15.6948			−6.79003			37.8264			12.1965			−37.4563			33.3861			33.0520
1.5	−4.62264			0.223641			13.3688			−5.07801			−1.03381			13.5633			−24.8183			−26.9500			23.4738
1.6	−3.79953			4.80997			6.43642			1.29866			−18.2756			−1.62019			5.94086			−3.86420			−4.93429
1.7	−3.55980			−3.90055			4.67220			−19.3357			13.8852			18.4314			11.8463			−11.7857			68.8313
1.8	−3.48032			−2.00729			4.11265			−5.42082			6.98601			−27.8265			13.5292			−22.9708			18.8662
1.9	−3.20015			−9.16277			2.24095			−10.3410			29.3222			5.43136			18.4298			56.9564			33.0929
1.10	−2.90122			6.23880			0.417058			15.8001			−18.1001			−9.46578			21.9998			11.9227			−45.8396
1.11	−2.83656			8.17655			0.0460816			−2.30923			−23.1933			3.15838			22.5618			39.8559			6.55028
1.12	−2.40771			−4.57703			−2.20293			18.4699			11.0201			11.7306			24.5657			−6.05084			−44.4701
1.13	−2.02818			−9.13071			−3.88650			−2.96871			18.5187			−15.4258			24.1079			56.3698			6.02107
1.14	−1.78462			−0.436688			−4.81514			13.8087			0.779321			−6.26730			22.8701			−26.8093			−24.6433
1.15	−1.63650			−2.06438			−5.32187			−14.3735			3.37836			−27.7797			21.8012			−22.7383			23.5223
1.16	−1.18198			−2.60560			−6.60292			−7.12046			3.07976			33.7625			17.2604			−20.2109			8.41624
1.17	−1.12752			9.49735			−6.72870			7.22240			−10.7085			−1.17565			16.6069			63.1996			−8.14341
1.18	−1.00172			−3.02985			−6.99655			20.0383			3.03507			−1.63570			15.0224			−17.8200			−20.0728
1.19	−0.532806			1.85539			−7.71612			−18.1107			−0.988563			−20.2803			8.37365			−23.5575			9.64951
1.20	−0.169295			6.82637			−7.97134			−1.80831			−1.15567			16.1277			2.70387			19.5993			0.306138

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.o	yes	39
13.b	even	2	1		1859.4.a.n	✓	39

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1859.4.a.n	✓	39	13.b	even	2	1
1859.4.a.o	yes	39	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^39 - 213*T2^37 + 7*T2^36 + 20695*T2^35 - 1070*T2^34 - 1215940*T2^33 + 69288*T2^32 + 48297883*T2^31 - 2389752*T2^30 - 1373688710*T2^29 + 41608817*T2^28 + 28913103950*T2^27 - 23146836*T2^26 - 459092123012*T2^25 - 17168426656*T2^24 + 5556687964643*T2^23 + 459171188888*T2^22 - 51468129676989*T2^21 - 6862014114335*T2^20 + 364264338755287*T2^19 + 68520874595634*T2^18 - 1956901678568496*T2^17 - 481224273904152*T2^16 + 7882704850912633*T2^15 + 2411433625662992*T2^14 - 23354424046750224*T2^13 - 8579711848903369*T2^12 + 49428196374256172*T2^11 + 21222250229812512*T2^10 - 71437011741332576*T2^9 - 35038070985309056*T2^8 + 65459584200543200*T2^7 + 35895565425104768*T2^6 - 33098105534121472*T2^5 - 19801875164434432*T2^4 + 6618498930894336*T2^3 + 4172426271754240*T2^2 - 88923785019392*T2 - 91431516471296