Newform orbit 1458.3.b.c

• Label: 1458.3.b.c
• Level: $1458$
• Weight: $3$
• Character orbit: 1458.b
• Analytic conductor: $39.728$
• Analytic rank: $0$
• Dimension: $36$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1458 = 2 \cdot 3^{6} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1458.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(39.7276225437\)
Analytic rank:	\(0\)
Dimension:	\(36\)
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 36 q - 72 q^{4} + 144 q^{16} - 180 q^{25} + 252 q^{49} - 36 q^{61} - 288 q^{64} + 180 q^{67} - 252 q^{73} + 396 q^{91}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1457.1		−	1.41421i		0		−2.00000				−	8.37465i		0		−11.2416					2.82843i		0		−11.8435
1457.2		−	1.41421i		0		−2.00000				−	8.36153i		0		9.16954					2.82843i		0		−11.8250
1457.3		−	1.41421i		0		−2.00000				−	7.83103i		0		−0.901000					2.82843i		0		−11.0748
1457.4		−	1.41421i		0		−2.00000				−	5.99439i		0		7.30820					2.82843i		0		−8.47735
1457.5		−	1.41421i		0		−2.00000				−	3.15510i		0		−1.44205					2.82843i		0		−4.46199
1457.6		−	1.41421i		0		−2.00000				−	2.89319i		0		−2.31381					2.82843i		0		−4.09159
1457.7		−	1.41421i		0		−2.00000				−	2.32339i		0		−6.28987					2.82843i		0		−3.28577
1457.8		−	1.41421i		0		−2.00000				−	2.03782i		0		12.8548					2.82843i		0		−2.88192
1457.9		−	1.41421i		0		−2.00000				−	0.904788i		0		−7.18058					2.82843i		0		−1.27956
1457.10		−	1.41421i		0		−2.00000				−	0.589631i		0		−3.15313					2.82843i		0		−0.833865
1457.11		−	1.41421i		0		−2.00000					1.13188i		0		−1.91375					2.82843i		0		1.60072
1457.12		−	1.41421i		0		−2.00000					3.04245i		0		8.22876					2.82843i		0		4.30268
1457.13		−	1.41421i		0		−2.00000					4.04819i		0		−13.2098					2.82843i		0		5.72501
1457.14		−	1.41421i		0		−2.00000					4.50363i		0		1.28890					2.82843i		0		6.36909
1457.15		−	1.41421i		0		−2.00000					5.53495i		0		10.9212					2.82843i		0		7.82759
1457.16		−	1.41421i		0		−2.00000					7.63957i		0		5.75438					2.82843i		0		10.8040
1457.17		−	1.41421i		0		−2.00000					7.93206i		0		0.453662					2.82843i		0		11.2176
1457.18		−	1.41421i		0		−2.00000					8.63280i		0		−8.33391					2.82843i		0		12.2086
1457.19			1.41421i		0		−2.00000				−	8.63280i		0		−8.33391				−	2.82843i		0		12.2086
1457.20			1.41421i		0		−2.00000				−	7.93206i		0		0.453662				−	2.82843i		0		11.2176

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1458.3.b.c		36
3.b	odd	2	1	inner	1458.3.b.c		36
27.e	even	9	1		54.3.f.a	✓	36
27.e	even	9	1		162.3.f.a		36
27.f	odd	18	1		54.3.f.a	✓	36
27.f	odd	18	1		162.3.f.a		36
108.j	odd	18	1		432.3.bc.c		36
108.l	even	18	1		432.3.bc.c		36

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
54.3.f.a	✓	36	27.e	even	9	1
54.3.f.a	✓	36	27.f	odd	18	1
162.3.f.a		36	27.e	even	9	1
162.3.f.a		36	27.f	odd	18	1
432.3.bc.c		36	108.j	odd	18	1
432.3.bc.c		36	108.l	even	18	1
1458.3.b.c		36	1.a	even	1	1	trivial
1458.3.b.c		36	3.b	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^36 + 540*T5^34 + 130950*T5^32 + 18848214*T5^30 + 1793815389*T5^28 + 119095414884*T5^26 + 5676157936791*T5^24 + 197071625014632*T5^22 + 5012659326804732*T5^20 + 93324747778494858*T5^18 + 1263541114529109171*T5^16 + 12288913660653962940*T5^14 + 84197203942506305193*T5^12 + 394449774873877258830*T5^10 + 1207328715560340217035*T5^8 + 2251182113230749907698*T5^6 + 2300185334472409888650*T5^4 + 1119009093522912382500*T5^2 + 189838550677028765625