Newform orbit 4015.2.a.e

• Label: 4015.2.a.e
• Level: $4015$
• Weight: $2$
• Character orbit: 4015.a
• Self dual: yes
• Analytic conductor: $32.060$
• Analytic rank: $0$
• Dimension: $27$
• 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:	\(0\)
Dimension:	\(27\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 27 q + 6 q^{2} + 5 q^{3} + 22 q^{4} - 27 q^{5} + 7 q^{6} + 10 q^{7} + 15 q^{8} + 24 q^{9}+O(q^{10}) \)

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	−2.34661			2.98114			3.50659			−1.00000			−6.99558			0.286679			−3.53537			5.88720			2.34661
1.2	−2.33465			−0.983408			3.45061			−1.00000			2.29592			−2.48043			−3.38668			−2.03291			2.33465
1.3	−2.24746			1.22256			3.05108			−1.00000			−2.74765			−0.859995			−2.36225			−1.50535			2.24746
1.4	−2.19462			−2.47425			2.81638			−1.00000			5.43004			3.64013			−1.79164			3.12189			2.19462
1.5	−1.64001			1.19849			0.689644			−1.00000			−1.96554			−2.90687			2.14900			−1.56361			1.64001
1.6	−1.49741			2.11504			0.242240			−1.00000			−3.16709			4.23699			2.63209			1.47340			1.49741
1.7	−1.35811			0.129284			−0.155539			−1.00000			−0.175582			−0.681246			2.92746			−2.98329			1.35811
1.8	−1.32466			−2.16018			−0.245282			−1.00000			2.86150			−3.08475			2.97423			1.66638			1.32466
1.9	−0.788550			−0.398652			−1.37819			−1.00000			0.314357			4.29459			2.66387			−2.84108			0.788550
1.10	−0.590698			0.738483			−1.65108			−1.00000			−0.436221			−1.02669			2.15668			−2.45464			0.590698
1.11	−0.339834			2.87141			−1.88451			−1.00000			−0.975803			0.914353			1.32009			5.24498			0.339834
1.12	−0.0879542			−2.14989			−1.99226			−1.00000			0.189092			3.99167			0.351137			1.62202			0.0879542
1.13	−0.0560878			−2.46183			−1.99685			−1.00000			0.138079			−2.79584			0.224175			3.06062			0.0560878
1.14	0.0645883			−2.75103			−1.99583			−1.00000			−0.177684			0.602441			−0.258084			4.56815			−0.0645883
1.15	0.782969			−1.17473			−1.38696			−1.00000			−0.919776			1.16812			−2.65188			−1.62001			−0.782969
1.16	0.924358			1.45154			−1.14556			−1.00000			1.34174			3.41942			−2.90763			−0.893034			−0.924358
1.17	0.966384			2.94159			−1.06610			−1.00000			2.84271			−4.68182			−2.96303			5.65296			−0.966384
1.18	1.13591			3.01832			−0.709697			−1.00000			3.42856			3.60395			−3.07799			6.11027			−1.13591
1.19	1.36344			−0.755926			−0.141019			−1.00000			−1.03066			1.53902			−2.91916			−2.42858			−1.36344
1.20	1.39893			−0.528085			−0.0429944			−1.00000			−0.738755			−3.55790			−2.85801			−2.72113			−1.39893

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.e	✓	27

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
4015.2.a.e	✓	27	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^27 - 6*T2^26 - 20*T2^25 + 179*T2^24 + 80*T2^23 - 2285*T2^22 + 1258*T2^21 + 16289*T2^20 - 17870*T2^19 - 70930*T2^18 + 106216*T2^17 + 193421*T2^16 - 365367*T2^15 - 322877*T2^14 + 782296*T2^13 + 298110*T2^12 - 1052705*T2^11 - 95893*T2^10 + 867463*T2^9 - 58336*T2^8 - 413271*T2^7 + 50005*T2^6 + 103837*T2^5 - 7862*T2^4 - 11069*T2^3 - 712*T2^2 + 46*T2 + 3