Newform orbit 1881.4.a.n

• Label: 1881.4.a.n
• Level: $1881$
• Weight: $4$
• Character orbit: 1881.a
• Self dual: yes
• Analytic conductor: $110.983$
• Analytic rank: $1$
• Dimension: $23$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$1881 = 3^{2} \cdot 11 \cdot 19$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	1881.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$110.982592721$
Analytic rank:	$1$
Dimension:	$23$
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.

$\operatorname{Tr}(f)(q) =$ 23 * q - 4 * q^2 + 96 * q^4 - 14 * q^7 - 48 * q^8 - 124 * q^10 + 253 * q^11 - 150 * q^13 - 152 * q^14 + 444 * q^16 + 68 * q^17 - 437 * q^19 - 80 * q^20 - 44 * q^22 - 414 * q^23 + 383 * q^25 - 464 * q^26 - 384 * q^28 - 604 * q^29 + 136 * q^31 - 448 * q^32 - 114 * q^34 - 312 * q^35 - 134 * q^37 + 76 * q^38 - 1518 * q^40 - 540 * q^41 - 742 * q^43 + 1056 * q^44 + 230 * q^46 - 426 * q^47 + 1059 * q^49 - 1322 * q^50 - 320 * q^52 - 1164 * q^53 - 5058 * q^56 + 2572 * q^58 - 1490 * q^59 - 666 * q^61 - 5010 * q^62 + 5582 * q^64 - 2836 * q^65 + 324 * q^67 + 656 * q^68 + 3226 * q^70 - 4188 * q^71 - 242 * q^73 - 4730 * q^74 - 1824 * q^76 - 154 * q^77 - 436 * q^79 - 4914 * q^80 - 52 * q^82 - 1322 * q^83 - 3650 * q^85 - 3298 * q^86 - 528 * q^88 - 1630 * q^89 + 876 * q^91 - 6110 * q^92 + 2494 * q^94 - 5162 * q^97 - 7876 * q^98

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	−5.51625				0		22.4290			12.5056				0		26.5097			−79.5940				0		−68.9841
1.2	−5.44577				0		21.6564			−12.7630				0		14.1692			−74.3694				0		69.5044
1.3	−4.84967				0		15.5193			5.07821				0		−27.4332			−36.4664				0		−24.6277
1.4	−4.03785				0		8.30426			18.4926				0		−30.6896			−1.22854				0		−74.6704
1.5	−3.86437				0		6.93335			−18.6357				0		18.3770			4.12194				0		72.0151
1.6	−3.55917				0		4.66767			13.9292				0		7.71246			11.8603				0		−49.5764
1.7	−2.75980				0		−0.383506			8.09155				0		12.8476			23.1368				0		−22.3311
1.8	−2.60095				0		−1.23504			−11.0151				0		−27.4794			24.0199				0		28.6498
1.9	−2.17478				0		−3.27032			−3.87793				0		−23.3092			24.5105				0		8.43364
1.10	−1.56050				0		−5.56485			−10.6391				0		30.8256			21.1679				0		16.6023
1.11	−1.38247				0		−6.08877			11.8409				0		−1.48593			19.4774				0		−16.3697
1.12	0.0446892				0		−7.99800			−0.125306				0		5.63643			−0.714939				0		−0.00559983
1.13	0.835942				0		−7.30120			5.65129				0		9.55255			−12.7909				0		4.72415
1.14	1.19481				0		−6.57244			−18.9479				0		−16.9659			−17.4112				0		−22.6391
1.15	1.41012				0		−6.01156			4.37661				0		−26.4649			−19.7580				0		6.17155
1.16	2.00341				0		−3.98634			18.6175				0		22.2095			−24.0136				0		37.2986
1.17	2.42520				0		−2.11842			−17.7335				0		22.8095			−24.5392				0		−43.0071
1.18	3.14294				0		1.87809			−1.64084				0		21.7927			−19.2408				0		−5.15705
1.19	3.80817				0		6.50217			1.32583				0		−7.58061			−5.70400				0		5.04899
1.20	3.85322				0		6.84732			11.1576				0		−16.2200			−4.44155				0		42.9927

Atkin-Lehner signs

$p$	Sign
$3$	$+1$
$11$	$-1$
$19$	$+1$

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	1881.4.a.n	✓	23
3.b	odd	2	1		1881.4.a.o	yes	23

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1881.4.a.n	✓	23	1.a	even	1	1	trivial
1881.4.a.o	yes	23	3.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^23 + 4*T2^22 - 132*T2^21 - 512*T2^20 + 7417*T2^19 + 27748*T2^18 - 232705*T2^17 - 833504*T2^16 + 4499003*T2^15 + 15256746*T2^14 - 55910980*T2^13 - 176281530*T2^12 + 453573485*T2^11 + 1289159350*T2^10 - 2402000479*T2^9 - 5829737950*T2^8 + 8205473582*T2^7 + 15442641936*T2^6 - 17501371560*T2^5 - 21425770720*T2^4 + 21319044736*T2^3 + 11606591616*T2^2 - 11282528640*T2 + 479213568