Newform orbit 4015.2.a.g

• Label: 4015.2.a.g
• Level: $4015$
• Weight: $2$
• Character orbit: 4015.a
• Self dual: yes
• Analytic conductor: $32.060$
• Analytic rank: $1$
• Dimension: $32$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(32.0599364115\)
Analytic rank:	\(1\)
Dimension:	\(32\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9}+O(q^{10}) \)

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	−2.80101			2.07520			5.84563			−1.00000			−5.81265			2.07490			−10.7716			1.30645			2.80101
1.2	−2.75666			−2.97515			5.59919			−1.00000			8.20149			1.32848			−9.92176			5.85152			2.75666
1.3	−2.62713			−1.17329			4.90182			−1.00000			3.08238			3.02645			−7.62347			−1.62339			2.62713
1.4	−2.55668			0.570205			4.53663			−1.00000			−1.45783			−4.65776			−6.48536			−2.67487			2.55668
1.5	−2.31178			−1.68436			3.34432			−1.00000			3.89386			−2.49479			−3.10778			−0.162937			2.31178
1.6	−2.06358			2.59950			2.25838			−1.00000			−5.36430			−1.01430			−0.533185			3.75743			2.06358
1.7	−2.01115			−3.15685			2.04473			−1.00000			6.34891			−3.03904			−0.0899564			6.96573			2.01115
1.8	−1.96967			2.18511			1.87958			−1.00000			−4.30394			1.92639			0.237186			1.77472			1.96967
1.9	−1.75190			−0.429918			1.06914			−1.00000			0.753172			3.79529			1.63077			−2.81517			1.75190
1.10	−1.71308			1.21665			0.934626			−1.00000			−2.08421			−4.29501			1.82507			−1.51977			1.71308
1.11	−1.50747			−0.655267			0.272451			−1.00000			0.987792			−1.30717			2.60422			−2.57063			1.50747
1.12	−0.962434			2.32544			−1.07372			−1.00000			−2.23808			2.98112			2.95825			2.40766			0.962434
1.13	−0.960547			−2.83486			−1.07735			−1.00000			2.72301			4.60653			2.95594			5.03641			0.960547
1.14	−0.763072			0.889359			−1.41772			−1.00000			−0.678645			2.40954			2.60797			−2.20904			0.763072
1.15	−0.711670			−2.33630			−1.49353			−1.00000			1.66268			−3.28922			2.48624			2.45831			0.711670
1.16	−0.193228			−1.07555			−1.96266			−1.00000			0.207825			1.51348			0.765696			−1.84320			0.193228
1.17	0.0852596			0.824276			−1.99273			−1.00000			0.0702774			0.193385			−0.340419			−2.32057			−0.0852596
1.18	0.338336			−0.770870			−1.88553			−1.00000			−0.260813			−3.60696			−1.31461			−2.40576			−0.338336
1.19	0.467946			3.03596			−1.78103			−1.00000			1.42067			−2.71430			−1.76932			6.21706			−0.467946
1.20	0.472050			−2.02631			−1.77717			−1.00000			−0.956522			−4.07098			−1.78301			1.10595			−0.472050

Atkin-Lehner signs

\( p \)	Sign
\(5\)	\( +1 \)
\(11\)	\( +1 \)
\(73\)	\( +1 \)

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	4015.2.a.g	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
4015.2.a.g	✓	32	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^32 + 5*T2^31 - 38*T2^30 - 219*T2^29 + 602*T2^28 + 4267*T2^27 - 4936*T2^26 - 48848*T2^25 + 18739*T2^24 + 365631*T2^23 + 20864*T2^22 - 1885002*T2^21 - 613517*T2^20 + 6873593*T2^19 + 3353980*T2^18 - 17941563*T2^17 - 10315953*T2^16 + 33599365*T2^15 + 20182520*T2^14 - 44905335*T2^13 - 25660565*T2^12 + 42286249*T2^11 + 20778429*T2^10 - 27417180*T2^9 - 10079045*T2^8 + 11737240*T2^7 + 2521893*T2^6 - 3047083*T2^5 - 172558*T2^4 + 392800*T2^3 - 29712*T2^2 - 12080*T2 + 1024