Newform orbit 1089.2.e.n

• Label: 1089.2.e.n
• Level: $1089$
• Weight: $2$
• Character orbit: 1089.e
• Analytic conductor: $8.696$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1089 = 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1089.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.69570878012\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) over \(\Q(\zeta_{3})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) 24 * q - 4 * q^4 + 6 * q^5 + 8 * q^9 + 20 * q^12 + 18 * q^14 + 26 * q^15 + 4 * q^16 + 24 * q^20 - 18 * q^23 - 2 * q^25 - 12 * q^26 + 54 * q^27 - 16 * q^31 - 26 * q^34 + 58 * q^36 - 8 * q^37 + 12 * q^38 - 16 * q^42 - 34 * q^45 + 30 * q^47 - 2 * q^48 + 8 * q^49 + 24 * q^53 - 30 * q^56 - 68 * q^58 + 30 * q^59 - 114 * q^60 - 32 * q^64 + 14 * q^67 - 70 * q^69 + 16 * q^70 - 156 * q^71 + 82 * q^75 + 12 * q^78 - 24 * q^80 + 104 * q^81 + 8 * q^82 + 18 * q^86 - 72 * q^89 + 24 * q^91 + 48 * q^92 - 28 * q^93 + 36 * q^97

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
364.1	−1.13819	−	1.97141i	−0.451577	−	1.67215i	−1.59097	+	2.75564i	−0.202501	+	0.350742i	−2.78251	+	2.79347i	0.976254	+	1.69092i	2.69056			−2.59216	+	1.51021i	0.921942
364.2	−1.13819	−	1.97141i	−1.01983	+	1.39998i	−1.59097	+	2.75564i	2.17391	−	3.76532i	3.92070	+	0.417061i	−0.317316	−	0.549607i	2.69056			−0.919882	−	2.85549i	−9.89733
364.3	−0.592963	−	1.02704i	1.71194	−	0.263165i	0.296790	−	0.514055i	−0.898979	+	1.55708i	−1.28540	−	1.60219i	1.75717	+	3.04351i	−3.07579			2.86149	−	0.901046i	2.13224
364.4	−0.592963	−	1.02704i	−0.184900	+	1.72215i	0.296790	−	0.514055i	−0.128063	+	0.221812i	1.87836	−	0.831274i	−0.492340	−	0.852757i	−3.07579			−2.93162	−	0.636851i	0.303747
364.5	−0.320794	−	0.555632i	1.67359	+	0.446216i	0.794182	−	1.37556i	1.27886	−	2.21505i	−0.288945	−	1.07304i	2.26057	+	3.91543i	−2.30225			2.60178	+	1.49356i	−1.64100
364.6	−0.320794	−	0.555632i	−1.72922	+	0.0990147i	0.794182	−	1.37556i	−0.723228	+	1.25267i	0.609739	+	0.929046i	0.0773729	+	0.134014i	−2.30225			2.98039	−	0.342436i	0.928030
364.7	0.320794	+	0.555632i	1.67359	+	0.446216i	0.794182	−	1.37556i	1.27886	−	2.21505i	0.288945	+	1.07304i	−2.26057	−	3.91543i	2.30225			2.60178	+	1.49356i	1.64100
364.8	0.320794	+	0.555632i	−1.72922	+	0.0990147i	0.794182	−	1.37556i	−0.723228	+	1.25267i	−0.609739	−	0.929046i	−0.0773729	−	0.134014i	2.30225			2.98039	−	0.342436i	−0.928030
364.9	0.592963	+	1.02704i	1.71194	−	0.263165i	0.296790	−	0.514055i	−0.898979	+	1.55708i	1.28540	+	1.60219i	−1.75717	−	3.04351i	3.07579			2.86149	−	0.901046i	−2.13224
364.10	0.592963	+	1.02704i	−0.184900	+	1.72215i	0.296790	−	0.514055i	−0.128063	+	0.221812i	−1.87836	+	0.831274i	0.492340	+	0.852757i	3.07579			−2.93162	−	0.636851i	−0.303747
364.11	1.13819	+	1.97141i	−1.01983	+	1.39998i	−1.59097	+	2.75564i	2.17391	−	3.76532i	−3.92070	−	0.417061i	0.317316	+	0.549607i	−2.69056			−0.919882	−	2.85549i	9.89733
364.12	1.13819	+	1.97141i	−0.451577	−	1.67215i	−1.59097	+	2.75564i	−0.202501	+	0.350742i	2.78251	−	2.79347i	−0.976254	−	1.69092i	−2.69056			−2.59216	+	1.51021i	−0.921942
727.1	−1.13819	+	1.97141i	−0.451577	+	1.67215i	−1.59097	−	2.75564i	−0.202501	−	0.350742i	−2.78251	−	2.79347i	0.976254	−	1.69092i	2.69056			−2.59216	−	1.51021i	0.921942
727.2	−1.13819	+	1.97141i	−1.01983	−	1.39998i	−1.59097	−	2.75564i	2.17391	+	3.76532i	3.92070	−	0.417061i	−0.317316	+	0.549607i	2.69056			−0.919882	+	2.85549i	−9.89733
727.3	−0.592963	+	1.02704i	1.71194	+	0.263165i	0.296790	+	0.514055i	−0.898979	−	1.55708i	−1.28540	+	1.60219i	1.75717	−	3.04351i	−3.07579			2.86149	+	0.901046i	2.13224
727.4	−0.592963	+	1.02704i	−0.184900	−	1.72215i	0.296790	+	0.514055i	−0.128063	−	0.221812i	1.87836	+	0.831274i	−0.492340	+	0.852757i	−3.07579			−2.93162	+	0.636851i	0.303747
727.5	−0.320794	+	0.555632i	1.67359	−	0.446216i	0.794182	+	1.37556i	1.27886	+	2.21505i	−0.288945	+	1.07304i	2.26057	−	3.91543i	−2.30225			2.60178	−	1.49356i	−1.64100
727.6	−0.320794	+	0.555632i	−1.72922	−	0.0990147i	0.794182	+	1.37556i	−0.723228	−	1.25267i	0.609739	−	0.929046i	0.0773729	−	0.134014i	−2.30225			2.98039	+	0.342436i	0.928030
727.7	0.320794	−	0.555632i	1.67359	−	0.446216i	0.794182	+	1.37556i	1.27886	+	2.21505i	0.288945	−	1.07304i	−2.26057	+	3.91543i	2.30225			2.60178	−	1.49356i	1.64100
727.8	0.320794	−	0.555632i	−1.72922	−	0.0990147i	0.794182	+	1.37556i	−0.723228	−	1.25267i	−0.609739	+	0.929046i	−0.0773729	+	0.134014i	2.30225			2.98039	+	0.342436i	−0.928030

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
9.c	even	3	1	inner
11.b	odd	2	1	inner
99.h	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1089.2.e.n	✓	24
9.c	even	3	1	inner	1089.2.e.n	✓	24
9.c	even	3	1		9801.2.a.ch		12
9.d	odd	6	1		9801.2.a.ci		12
11.b	odd	2	1	inner	1089.2.e.n	✓	24
99.g	even	6	1		9801.2.a.ci		12
99.h	odd	6	1	inner	1089.2.e.n	✓	24
99.h	odd	6	1		9801.2.a.ch		12

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1089.2.e.n	✓	24	1.a	even	1	1	trivial
1089.2.e.n	✓	24	9.c	even	3	1	inner
1089.2.e.n	✓	24	11.b	odd	2	1	inner
1089.2.e.n	✓	24	99.h	odd	6	1	inner
9801.2.a.ch		12	9.c	even	3	1
9801.2.a.ch		12	99.h	odd	6	1
9801.2.a.ci		12	9.d	odd	6	1
9801.2.a.ci		12	99.g	even	6	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(1089, [\chi])\):

\( T_{2}^{12} + 7T_{2}^{10} + 39T_{2}^{8} + 64T_{2}^{6} + 79T_{2}^{4} + 30T_{2}^{2} + 9 \)

T5^12 - 3*T5^11 + 20*T5^10 + 9*T5^9 + 117*T5^8 + 129*T5^7 + 653*T5^6 + 933*T5^5 + 1381*T5^4 + 768*T5^3 + 321*T5^2 + 63*T5 + 9