Newform orbit 945.2.cc.b

• Label: 945.2.cc.b
• Level: $945$
• Weight: $2$
• Character orbit: 945.cc
• Analytic conductor: $7.546$
• Analytic rank: $0$
• Dimension: $128$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.cc (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.54586299101\)
Analytic rank:	\(0\)
Dimension:	\(128\)
Relative dimension:	\(32\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 128 q + 4 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
82.1	−2.60718	+	0.698592i		0		4.57732	−	2.64271i	2.11398	−	0.728763i		0		2.07512	−	1.64130i	−6.27053	+	6.27053i		0		−5.00242	+	3.37683i
82.2	−2.49621	+	0.668856i		0		4.05163	−	2.33921i	0.526131	+	2.17329i		0		0.993488	+	2.45214i	−4.89440	+	4.89440i		0		−2.76695	−	5.07307i
82.3	−2.33558	+	0.625816i		0		3.33123	−	1.92329i	−1.14918	+	1.91817i		0		−2.17647	−	1.50431i	−3.15720	+	3.15720i		0		1.48357	−	5.19922i
82.4	−2.30176	+	0.616755i		0		3.18567	−	1.83925i	0.0431322	−	2.23565i		0		−1.76305	+	1.97273i	−2.82827	+	2.82827i		0		1.27957	+	5.17254i
82.5	−2.30162	+	0.616717i		0		3.18506	−	1.83889i	−2.21935	−	0.272932i		0		1.10114	−	2.40572i	−2.82691	+	2.82691i		0		5.27642	−	0.740523i
82.6	−1.85259	+	0.496400i		0		1.45363	−	0.839251i	2.11600	−	0.722869i		0		−1.79662	+	1.94220i	0.436013	−	0.436013i		0		−3.56125	+	2.38956i
82.7	−1.78393	+	0.478003i		0		1.22187	−	0.705449i	−1.34508	−	1.78627i		0		2.63937	+	0.183594i	0.769325	−	0.769325i		0		3.25337	+	2.54363i
82.8	−1.54799	+	0.414782i		0		0.492166	−	0.284152i	−1.80256	+	1.32317i		0		0.406767	+	2.61430i	1.62240	−	1.62240i		0		2.24151	−	2.79592i
82.9	−1.50306	+	0.402743i		0		0.364926	−	0.210690i	2.23119	+	0.147619i		0		2.54926	+	0.708003i	1.73698	−	1.73698i		0		−3.41306	+	0.676715i
82.10	−1.24720	+	0.334186i		0		−0.288222	+	0.166405i	1.08769	−	1.95370i		0		−0.415131	−	2.61298i	2.12989	−	2.12989i		0		−0.703668	+	2.80014i
82.11	−1.19853	+	0.321146i		0		−0.398708	+	0.230194i	−0.315896	+	2.21364i		0		−2.40170	+	1.10988i	2.15871	−	2.15871i		0		−0.332290	−	2.75457i
82.12	−0.841389	+	0.225450i		0		−1.07494	+	0.620618i	−1.10218	−	1.94556i		0		−1.45683	−	2.20854i	1.99641	−	1.99641i		0		1.36599	+	1.38849i
82.13	−0.678861	+	0.181900i		0		−1.30429	+	0.753030i	2.06655	+	0.854024i		0		−1.83294	−	1.90796i	1.74238	−	1.74238i		0		−1.55825	−	0.203857i
82.14	−0.478002	+	0.128080i		0		−1.51997	+	0.877555i	−1.39941	+	1.74403i		0		2.33264	−	1.24852i	1.31399	−	1.31399i		0		0.445546	−	1.01289i
82.15	−0.200481	+	0.0537188i		0		−1.69474	+	0.978461i	−1.03275	−	1.98329i		0		1.42181	+	2.23125i	0.580728	−	0.580728i		0		0.313587	+	0.342134i
82.16	−0.0793398	+	0.0212590i		0		−1.72621	+	0.996627i	−2.23562	−	0.0448193i		0		−2.04287	+	1.68128i	0.231931	−	0.231931i		0		0.178326	−	0.0439712i
82.17	0.0793398	−	0.0212590i		0		−1.72621	+	0.996627i	2.23562	+	0.0448193i		0		−2.04287	+	1.68128i	−0.231931	+	0.231931i		0		0.178326	−	0.0439712i
82.18	0.200481	−	0.0537188i		0		−1.69474	+	0.978461i	1.03275	+	1.98329i		0		1.42181	+	2.23125i	−0.580728	+	0.580728i		0		0.313587	+	0.342134i
82.19	0.478002	−	0.128080i		0		−1.51997	+	0.877555i	1.39941	−	1.74403i		0		2.33264	−	1.24852i	−1.31399	+	1.31399i		0		0.445546	−	1.01289i
82.20	0.678861	−	0.181900i		0		−1.30429	+	0.753030i	−2.06655	−	0.854024i		0		−1.83294	−	1.90796i	−1.74238	+	1.74238i		0		−1.55825	−	0.203857i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
5.c	odd	4	1	inner
7.d	odd	6	1	inner
15.e	even	4	1	inner
21.g	even	6	1	inner
35.k	even	12	1	inner
105.w	odd	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	945.2.cc.b	✓	128
3.b	odd	2	1	inner	945.2.cc.b	✓	128
5.c	odd	4	1	inner	945.2.cc.b	✓	128
7.d	odd	6	1	inner	945.2.cc.b	✓	128
15.e	even	4	1	inner	945.2.cc.b	✓	128
21.g	even	6	1	inner	945.2.cc.b	✓	128
35.k	even	12	1	inner	945.2.cc.b	✓	128
105.w	odd	12	1	inner	945.2.cc.b	✓	128

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
945.2.cc.b	✓	128	1.a	even	1	1	trivial
945.2.cc.b	✓	128	3.b	odd	2	1	inner
945.2.cc.b	✓	128	5.c	odd	4	1	inner
945.2.cc.b	✓	128	7.d	odd	6	1	inner
945.2.cc.b	✓	128	15.e	even	4	1	inner
945.2.cc.b	✓	128	21.g	even	6	1	inner
945.2.cc.b	✓	128	35.k	even	12	1	inner
945.2.cc.b	✓	128	105.w	odd	12	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^128 - 240*T2^124 + 33032*T2^120 - 3086480*T2^116 + 216977332*T2^112 - 11903638722*T2^108 + 524772136640*T2^104 - 18797293269728*T2^100 + 552507172496690*T2^96 - 13334428932060096*T2^92 + 264768772156890155*T2^88 - 4306881536210881528*T2^84 + 57415100332846696616*T2^80 - 623804291478801781074*T2^76 + 5517652174562548654432*T2^72 - 39387439456410438916562*T2^68 + 226261884065882373701987*T2^64 - 1030911312752346280238144*T2^60 + 3700054822150490588638998*T2^56 - 10183955319063464488123796*T2^52 + 21344156181616826496525121*T2^48 - 32213222059655247223700774*T2^44 + 34319417514281951195937444*T2^40 - 21561332804653839779768716*T2^36 + 9465645017586229461470642*T2^32 - 2200755378625594132874684*T2^28 + 355525333594314210843638*T2^24 - 19989987799639836989864*T2^20 + 845871364186463097932*T2^16 - 1604300122333761020*T2^12 + 2855325971856288*T2^8 - 129891084344*T2^4 + 5764801