Newform orbit 3021.2.a.k

• Label: 3021.2.a.k
• Level: $3021$
• Weight: $2$
• Character orbit: 3021.a
• Self dual: yes
• Analytic conductor: $24.123$
• Analytic rank: $0$
• Dimension: $25$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 3021 = 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3021.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(24.1228064506\)
Analytic rank:	\(0\)
Dimension:	\(25\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 25 q - 5 q^{2} - 25 q^{3} + 31 q^{4} + 3 q^{5} + 5 q^{6} + 12 q^{7} - 15 q^{8} + 25 q^{9}+O(q^{10}) \)

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	−2.75933			−1.00000			5.61389			3.61252			2.75933			3.28567			−9.97191			1.00000			−9.96814
1.2	−2.72274			−1.00000			5.41334			2.31234			2.72274			−4.68431			−9.29365			1.00000			−6.29592
1.3	−2.65882			−1.00000			5.06934			−4.09638			2.65882			−1.15395			−8.16084			1.00000			10.8916
1.4	−2.58229			−1.00000			4.66823			−1.37967			2.58229			4.86016			−6.89014			1.00000			3.56272
1.5	−2.10035			−1.00000			2.41149			−3.40505			2.10035			1.59524			−0.864264			1.00000			7.15181
1.6	−1.96607			−1.00000			1.86543			−0.0519176			1.96607			−2.09958			0.264575			1.00000			0.102074
1.7	−1.95238			−1.00000			1.81180			2.53145			1.95238			0.628097			0.367430			1.00000			−4.94236
1.8	−1.61078			−1.00000			0.594602			3.61998			1.61078			3.57915			2.26378			1.00000			−5.83098
1.9	−1.18630			−1.00000			−0.592700			−0.105869			1.18630			−3.09686			3.07571			1.00000			0.125592
1.10	−0.940269			−1.00000			−1.11590			−3.19704			0.940269			−1.58083			2.92978			1.00000			3.00608
1.11	−0.689782			−1.00000			−1.52420			−3.26943			0.689782			1.57379			2.43093			1.00000			2.25519
1.12	−0.488091			−1.00000			−1.76177			1.71719			0.488091			−2.45993			1.83608			1.00000			−0.838147
1.13	−0.360697			−1.00000			−1.86990			−1.77217			0.360697			1.06491			1.39586			1.00000			0.639217
1.14	−0.337113			−1.00000			−1.88636			2.96362			0.337113			0.274329			1.31014			1.00000			−0.999074
1.15	−0.0104466			−1.00000			−1.99989			0.182515			0.0104466			4.90426			0.0417851			1.00000			−0.00190665
1.16	0.810921			−1.00000			−1.34241			−1.02563			−0.810921			2.68951			−2.71043			1.00000			−0.831706
1.17	0.901802			−1.00000			−1.18675			1.72877			−0.901802			−1.95363			−2.87382			1.00000			1.55901
1.18	1.02726			−1.00000			−0.944734			4.34947			−1.02726			2.14827			−3.02501			1.00000			4.46804
1.19	1.52806			−1.00000			0.334967			−1.73395			−1.52806			−3.58375			−2.54427			1.00000			−2.64959
1.20	1.57668			−1.00000			0.485925			−1.93058			−1.57668			−3.62511			−2.38721			1.00000			−3.04391

Atkin-Lehner signs

\( p \)	Sign
\(3\)	\(1\)
\(19\)	\(-1\)
\(53\)	\(1\)

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	3021.2.a.k	✓	25
3.b	odd	2	1		9063.2.a.p		25

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
3021.2.a.k	✓	25	1.a	even	1	1	trivial
9063.2.a.p		25	3.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^25 + 5*T2^24 - 28*T2^23 - 170*T2^22 + 290*T2^21 + 2471*T2^20 - 1035*T2^19 - 20062*T2^18 - 4389*T2^17 + 99755*T2^16 + 60069*T2^15 - 313089*T2^14 - 272480*T2^13 + 614570*T2^12 + 675691*T2^11 - 712686*T2^10 - 981797*T2^9 + 408125*T2^8 + 816938*T2^7 - 20018*T2^6 - 349893*T2^5 - 86770*T2^4 + 52933*T2^3 + 27929*T2^2 + 3732*T2 + 36