Newform orbit 4015.2.a.b

• Label: 4015.2.a.b
• Level: $4015$
• Weight: $2$
• Character orbit: 4015.a
• Self dual: yes
• Analytic conductor: $32.060$
• Analytic rank: $1$
• Dimension: $23$
• 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:	\(23\)
Twist minimal:	yes
Fricke sign:	\(1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) \)

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	−2.71506			1.57103			5.37156			1.00000			−4.26545			1.27925			−9.15401			−0.531858			−2.71506
1.2	−2.35657			2.73189			3.55343			1.00000			−6.43790			−2.31150			−3.66076			4.46323			−2.35657
1.3	−2.32698			−0.285099			3.41485			1.00000			0.663421			−4.31195			−3.29232			−2.91872			−2.32698
1.4	−2.28085			−0.867872			3.20226			1.00000			1.97948			0.729352			−2.74217			−2.24680			−2.28085
1.5	−2.06292			0.357225			2.25565			1.00000			−0.736927			1.84250			−0.527390			−2.87239			−2.06292
1.6	−1.83447			−2.15866			1.36527			1.00000			3.95999			0.444043			1.16439			1.65981			−1.83447
1.7	−1.19799			1.69638			−0.564821			1.00000			−2.03224			−2.11615			3.07263			−0.122309			−1.19799
1.8	−1.16229			1.36223			−0.649085			1.00000			−1.58330			3.38995			3.07900			−1.14434			−1.16229
1.9	−1.09501			−2.94583			−0.800943			1.00000			3.22573			2.47152			3.06707			5.67794			−1.09501
1.10	−1.08357			−1.29689			−0.825886			1.00000			1.40527			−5.06508			3.06203			−1.31806			−1.08357
1.11	−0.654679			2.96699			−1.57140			1.00000			−1.94243			−1.18438			2.33812			5.80304			−0.654679
1.12	−0.182665			1.60195			−1.96663			1.00000			−0.292620			−3.46851			0.724566			−0.433762			−0.182665
1.13	0.152616			−0.242697			−1.97671			1.00000			−0.0370393			2.57515			−0.606909			−2.94110			0.152616
1.14	0.152825			−1.31847			−1.97664			1.00000			−0.201495			−0.959999			−0.607731			−1.26164			0.152825
1.15	0.430868			−1.25921			−1.81435			1.00000			−0.542554			4.34543			−1.64348			−1.41438			0.430868
1.16	0.772478			−3.03398			−1.40328			1.00000			−2.34368			1.44909			−2.62896			6.20504			0.772478
1.17	1.18208			−1.23608			−0.602686			1.00000			−1.46115			−1.06876			−3.07658			−1.47210			1.18208
1.18	1.32991			2.72450			−0.231346			1.00000			3.62333			−4.53918			−2.96748			4.42288			1.32991
1.19	1.55677			0.976240			0.423526			1.00000			1.51978			−0.0535957			−2.45420			−2.04696			1.55677
1.20	1.79465			0.618778			1.22075			1.00000			1.11049			1.73339			−1.39847			−2.61711			1.79465

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.b	✓	23

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
4015.2.a.b	✓	23	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^23 + 5*T2^22 - 18*T2^21 - 121*T2^20 + 95*T2^19 + 1226*T2^18 + 170*T2^17 - 6777*T2^16 - 4008*T2^15 + 22317*T2^14 + 19176*T2^13 - 44845*T2^12 - 46653*T2^11 + 54086*T2^10 + 63814*T2^9 - 37050*T2^8 - 48152*T2^7 + 13175*T2^6 + 18072*T2^5 - 2433*T2^4 - 2661*T2^3 + 330*T2^2 + 69*T2 - 9