Newform orbit 6015.2.a.e

• Label: 6015.2.a.e
• Level: $6015$
• Weight: $2$
• Character orbit: 6015.a
• Self dual: yes
• Analytic conductor: $48.030$
• Analytic rank: $0$
• Dimension: $31$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(48.0300168158\)
Analytic rank:	\(0\)
Dimension:	\(31\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9}+O(q^{10}) \)

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	−2.46359			−1.00000			4.06929			−1.00000			2.46359			−1.56442			−5.09790			1.00000			2.46359
1.2	−2.32925			−1.00000			3.42539			−1.00000			2.32925			−3.29161			−3.32009			1.00000			2.32925
1.3	−2.16689			−1.00000			2.69543			−1.00000			2.16689			0.00504296			−1.50693			1.00000			2.16689
1.4	−2.16128			−1.00000			2.67112			−1.00000			2.16128			1.73409			−1.45047			1.00000			2.16128
1.5	−2.02086			−1.00000			2.08386			−1.00000			2.02086			0.941480			−0.169465			1.00000			2.02086
1.6	−1.61585			−1.00000			0.610967			−1.00000			1.61585			5.09249			2.24447			1.00000			1.61585
1.7	−1.60901			−1.00000			0.588914			−1.00000			1.60901			−4.04417			2.27045			1.00000			1.60901
1.8	−1.52097			−1.00000			0.313357			−1.00000			1.52097			−2.49520			2.56534			1.00000			1.52097
1.9	−1.22966			−1.00000			−0.487935			−1.00000			1.22966			−1.61954			3.05932			1.00000			1.22966
1.10	−0.900767			−1.00000			−1.18862			−1.00000			0.900767			3.65606			2.87220			1.00000			0.900767
1.11	−0.707695			−1.00000			−1.49917			−1.00000			0.707695			−2.27723			2.47634			1.00000			0.707695
1.12	−0.349021			−1.00000			−1.87818			−1.00000			0.349021			0.242299			1.35357			1.00000			0.349021
1.13	−0.325483			−1.00000			−1.89406			−1.00000			0.325483			−4.65914			1.26745			1.00000			0.325483
1.14	−0.0812850			−1.00000			−1.99339			−1.00000			0.0812850			2.03254			0.324603			1.00000			0.0812850
1.15	0.0495237			−1.00000			−1.99755			−1.00000			−0.0495237			−1.50762			−0.197974			1.00000			−0.0495237
1.16	0.0951324			−1.00000			−1.99095			−1.00000			−0.0951324			0.303287			−0.379669			1.00000			−0.0951324
1.17	0.363417			−1.00000			−1.86793			−1.00000			−0.363417			3.29378			−1.40567			1.00000			−0.363417
1.18	0.698893			−1.00000			−1.51155			−1.00000			−0.698893			4.36738			−2.45420			1.00000			−0.698893
1.19	0.917882			−1.00000			−1.15749			−1.00000			−0.917882			−0.377330			−2.89821			1.00000			−0.917882
1.20	1.04920			−1.00000			−0.899176			−1.00000			−1.04920			2.71724			−3.04182			1.00000			−1.04920

Atkin-Lehner signs

\( p \)	Sign
\(3\)	\(1\)
\(5\)	\(1\)
\(401\)	\(-1\)

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	6015.2.a.e	✓	31

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
6015.2.a.e	✓	31	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^31 - 6*T2^30 - 25*T2^29 + 209*T2^28 + 182*T2^27 - 3192*T2^26 + 818*T2^25 + 28074*T2^24 - 24022*T2^23 - 156917*T2^22 + 198498*T2^21 + 579410*T2^20 - 934955*T2^19 - 1418349*T2^18 + 2826745*T2^17 + 2226788*T2^16 - 5668399*T2^15 - 2011405*T2^14 + 7521922*T2^13 + 623993*T2^12 - 6429553*T2^11 + 552274*T2^10 + 3360309*T2^9 - 594812*T2^8 - 987445*T2^7 + 195962*T2^6 + 142738*T2^5 - 21403*T2^4 - 8104*T2^3 + 629*T2^2 + 51*T2 - 3