Newform orbit 2031.4.a.d

• Label: 2031.4.a.d
• Level: $2031$
• Weight: $4$
• Character orbit: 2031.a
• Self dual: yes
• Analytic conductor: $119.833$
• Analytic rank: $0$
• Dimension: $94$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$2031 = 3 \cdot 677$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	2031.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$119.832879222$
Analytic rank:	$0$
Dimension:	$94$
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.

$\operatorname{Tr}(f)(q) =$ 94 * q + 19 * q^2 + 282 * q^3 + 409 * q^4 + 84 * q^5 + 57 * q^6 + 39 * q^7 + 228 * q^8 + 846 * q^9 + 145 * q^10 + 357 * q^11 + 1227 * q^12 + 271 * q^13 + 366 * q^14 + 252 * q^15 + 1865 * q^16 + 690 * q^17 + 171 * q^18 + 345 * q^19 + 939 * q^20 + 117 * q^21 + 148 * q^22 + 1135 * q^23 + 684 * q^24 + 3280 * q^25 + 1261 * q^26 + 2538 * q^27 + 214 * q^28 + 1396 * q^29 + 435 * q^30 + 889 * q^31 + 2048 * q^32 + 1071 * q^33 + 1590 * q^34 + 2104 * q^35 + 3681 * q^36 + 711 * q^37 + 2075 * q^38 + 813 * q^39 + 1675 * q^40 + 2931 * q^41 + 1098 * q^42 + 585 * q^43 + 4058 * q^44 + 756 * q^45 + 1148 * q^46 + 2733 * q^47 + 5595 * q^48 + 8415 * q^49 + 2640 * q^50 + 2070 * q^51 + 2174 * q^52 + 3430 * q^53 + 513 * q^54 + 2458 * q^55 + 4034 * q^56 + 1035 * q^57 + 259 * q^58 + 5376 * q^59 + 2817 * q^60 + 2064 * q^61 + 3610 * q^62 + 351 * q^63 + 10194 * q^64 + 5442 * q^65 + 444 * q^66 + 1429 * q^67 + 6932 * q^68 + 3405 * q^69 + 3888 * q^70 + 5336 * q^71 + 2052 * q^72 + 2412 * q^73 + 5911 * q^74 + 9840 * q^75 + 5988 * q^76 + 7100 * q^77 + 3783 * q^78 + 2018 * q^79 + 8054 * q^80 + 7614 * q^81 + 3546 * q^82 + 6229 * q^83 + 642 * q^84 + 2728 * q^85 + 6619 * q^86 + 4188 * q^87 + 3679 * q^88 + 11972 * q^89 + 1305 * q^90 + 5586 * q^91 + 15073 * q^92 + 2667 * q^93 + 3650 * q^94 + 8168 * q^95 + 6144 * q^96 + 5859 * q^97 + 8121 * q^98 + 3213 * 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	−5.47214			3.00000			21.9443			21.3352			−16.4164			−0.0652059			−76.3050			9.00000			−116.749
1.2	−5.45637			3.00000			21.7719			−6.07049			−16.3691			10.9617			−75.1446			9.00000			33.1228
1.3	−5.27921			3.00000			19.8701			11.0881			−15.8376			−17.2827			−62.6647			9.00000			−58.5362
1.4	−5.16569			3.00000			18.6843			17.7056			−15.4971			11.4525			−55.1919			9.00000			−91.4614
1.5	−5.10408			3.00000			18.0516			−3.79340			−15.3122			−8.15158			−51.3044			9.00000			19.3618
1.6	−5.10333			3.00000			18.0440			−16.6972			−15.3100			−10.1248			−51.2578			9.00000			85.2116
1.7	−5.02302			3.00000			17.2308			−13.6796			−15.0691			−35.1340			−46.3664			9.00000			68.7130
1.8	−4.91474			3.00000			16.1547			−10.0566			−14.7442			−7.95652			−40.0782			9.00000			49.4258
1.9	−4.76129			3.00000			14.6699			−4.67891			−14.2839			−10.6034			−31.7573			9.00000			22.2776
1.10	−4.72829			3.00000			14.3567			4.12529			−14.1849			15.0339			−30.0563			9.00000			−19.5056
1.11	−4.55506			3.00000			12.7486			8.74592			−13.6652			18.2953			−21.6301			9.00000			−39.8382
1.12	−4.50669			3.00000			12.3103			−0.307147			−13.5201			−10.6842			−19.4251			9.00000			1.38422
1.13	−4.45057			3.00000			11.8076			−1.33582			−13.3517			34.8098			−16.9459			9.00000			5.94516
1.14	−4.31352			3.00000			10.6064			−16.4491			−12.9406			−15.0796			−11.2430			9.00000			70.9536
1.15	−4.22592			3.00000			9.85844			−6.75739			−12.6778			30.5747			−7.85362			9.00000			28.5562
1.16	−4.09444			3.00000			8.76443			−8.00283			−12.2833			3.11074			−3.12990			9.00000			32.7671
1.17	−3.94499			3.00000			7.56296			15.3322			−11.8350			−27.0568			1.72411			9.00000			−60.4854
1.18	−3.73151			3.00000			5.92420			21.2295			−11.1945			17.7615			7.74587			9.00000			−79.2182
1.19	−3.42427			3.00000			3.72561			7.87027			−10.2728			−22.7257			14.6366			9.00000			−26.9499
1.20	−3.26684			3.00000			2.67224			21.8684			−9.80052			−22.0772			17.4049			9.00000			−71.4405

Atkin-Lehner signs

$p$	Sign
$3$	$-1$
$677$	$-1$

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	2031.4.a.d	✓	94

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2031.4.a.d	✓	94	1.a	even	1	1	trivial