Newform orbit 4034.2.a.b

• Label: 4034.2.a.b
• Level: $4034$
• Weight: $2$
• Character orbit: 4034.a
• Self dual: yes
• Analytic conductor: $32.212$
• Analytic rank: $1$
• Dimension: $35$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$4034 = 2 \cdot 2017$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	4034.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$32.2116521754$
Analytic rank:	$1$
Dimension:	$35$
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.

$\operatorname{Tr}(f)(q) =$ 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9 - 6 * q^10 - 9 * q^11 - 6 * q^12 - 7 * q^13 + 14 * q^14 - 19 * q^15 + 35 * q^16 + 17 * q^17 - 23 * q^18 - 25 * q^19 + 6 * q^20 - 15 * q^21 + 9 * q^22 - 12 * q^23 + 6 * q^24 + 7 * q^25 + 7 * q^26 - 27 * q^27 - 14 * q^28 - 13 * q^29 + 19 * q^30 - 69 * q^31 - 35 * q^32 + q^33 - 17 * q^34 - 4 * q^35 + 23 * q^36 - 22 * q^37 + 25 * q^38 - 38 * q^39 - 6 * q^40 + 15 * q^42 - 32 * q^43 - 9 * q^44 + 9 * q^45 + 12 * q^46 - 18 * q^47 - 6 * q^48 - 19 * q^49 - 7 * q^50 - 21 * q^51 - 7 * q^52 + 20 * q^53 + 27 * q^54 - 54 * q^55 + 14 * q^56 + 28 * q^57 + 13 * q^58 - 21 * q^59 - 19 * q^60 - 67 * q^61 + 69 * q^62 - 28 * q^63 + 35 * q^64 + 22 * q^65 - q^66 - 18 * q^67 + 17 * q^68 - 42 * q^69 + 4 * q^70 - 36 * q^71 - 23 * q^72 - 18 * q^73 + 22 * q^74 - 49 * q^75 - 25 * q^76 + 20 * q^77 + 38 * q^78 - 92 * q^79 + 6 * q^80 - 25 * q^81 + 42 * q^83 - 15 * q^84 - 29 * q^85 + 32 * q^86 - 40 * q^87 + 9 * q^88 - 8 * q^89 - 9 * q^90 - 89 * q^91 - 12 * q^92 - q^93 + 18 * q^94 - 62 * q^95 + 6 * q^96 - 40 * q^97 + 19 * q^98 - 64 * 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	−1.00000			−3.27997			1.00000			2.11941			3.27997			−0.124927			−1.00000			7.75819			−2.11941
1.2	−1.00000			−3.25702			1.00000			−1.18968			3.25702			1.65832			−1.00000			7.60820			1.18968
1.3	−1.00000			−2.93683			1.00000			0.0231797			2.93683			−4.16598			−1.00000			5.62497			−0.0231797
1.4	−1.00000			−2.83579			1.00000			4.39396			2.83579			−1.33504			−1.00000			5.04172			−4.39396
1.5	−1.00000			−2.39986			1.00000			−1.11547			2.39986			2.17590			−1.00000			2.75933			1.11547
1.6	−1.00000			−2.23091			1.00000			1.94904			2.23091			1.55699			−1.00000			1.97697			−1.94904
1.7	−1.00000			−2.01951			1.00000			3.52220			2.01951			−0.0194784			−1.00000			1.07840			−3.52220
1.8	−1.00000			−1.96432			1.00000			−0.678471			1.96432			4.37365			−1.00000			0.858567			0.678471
1.9	−1.00000			−1.95232			1.00000			−1.60299			1.95232			−2.46247			−1.00000			0.811553			1.60299
1.10	−1.00000			−1.90524			1.00000			−3.49980			1.90524			−2.88392			−1.00000			0.629935			3.49980
1.11	−1.00000			−1.74374			1.00000			−3.34943			1.74374			0.122108			−1.00000			0.0406325			3.34943
1.12	−1.00000			−1.52925			1.00000			3.51675			1.52925			−1.62140			−1.00000			−0.661396			−3.51675
1.13	−1.00000			−1.35256			1.00000			−0.395568			1.35256			1.50560			−1.00000			−1.17057			0.395568
1.14	−1.00000			−1.19422			1.00000			1.77357			1.19422			2.63831			−1.00000			−1.57384			−1.77357
1.15	−1.00000			−0.841269			1.00000			−1.88225			0.841269			−4.21612			−1.00000			−2.29227			1.88225
1.16	−1.00000			−0.715791			1.00000			2.28149			0.715791			−4.66835			−1.00000			−2.48764			−2.28149
1.17	−1.00000			−0.237603			1.00000			3.33211			0.237603			4.34322			−1.00000			−2.94355			−3.33211
1.18	−1.00000			0.00791248			1.00000			−2.05271			−0.00791248			−2.16347			−1.00000			−2.99994			2.05271
1.19	−1.00000			0.0555653			1.00000			0.675723			−0.0555653			−0.0958620			−1.00000			−2.99691			−0.675723
1.20	−1.00000			0.280261			1.00000			0.751535			−0.280261			1.30988			−1.00000			−2.92145			−0.751535

Atkin-Lehner signs

$p$	Sign
$2$	$+1$
$2017$	$+1$

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	4034.2.a.b	✓	35

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
4034.2.a.b	✓	35	1.a	even	1	1	trivial