Newform orbit 105.3.r.a

• Label: 105.3.r.a
• Level: $105$
• Weight: $3$
• Character orbit: 105.r
• Analytic conductor: $2.861$
• Analytic rank: $0$
• Dimension: $32$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.r (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.86104277578\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) 32 * q + 32 * q^4 - 6 * q^5 - 48 * q^9 + 78 * q^10 - 28 * q^11 + 60 * q^14 - 24 * q^15 - 40 * q^16 - 60 * q^19 + 12 * q^21 - 34 * q^25 - 96 * q^26 - 88 * q^29 + 84 * q^31 - 170 * q^35 - 192 * q^36 + 36 * q^39 + 330 * q^40 + 320 * q^44 + 18 * q^45 - 60 * q^46 + 356 * q^49 + 12 * q^51 - 468 * q^56 - 804 * q^59 - 198 * q^60 + 336 * q^61 - 400 * q^64 - 46 * q^65 - 108 * q^66 - 438 * q^70 + 344 * q^71 + 900 * q^74 + 144 * q^75 - 20 * q^79 + 1140 * q^80 - 144 * q^81 + 780 * q^84 + 304 * q^85 + 144 * q^86 + 24 * q^89 - 224 * q^91 - 924 * q^94 - 342 * q^95 + 900 * q^96 + 168 * q^99

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
19.1	−3.26825	−	1.88692i	0.866025	+	1.50000i	5.12097	+	8.86977i	−3.80462	+	3.24421i		−	6.53650i	−1.16497	−	6.90238i		−	23.5561i	−1.50000	+	2.59808i	18.5560	−	3.42385i
19.2	−2.95153	−	1.70407i	−0.866025	−	1.50000i	3.80769	+	6.59511i	−3.57204	−	3.49865i			5.90306i	−5.14807	+	4.74314i		−	12.3217i	−1.50000	+	2.59808i	4.58104	+	16.4134i
19.3	−2.53945	−	1.46615i	−0.866025	−	1.50000i	2.29920	+	3.98234i	1.01132	+	4.89665i			5.07890i	6.93149	+	0.976973i		−	1.75471i	−1.50000	+	2.59808i	4.61104	−	13.9176i
19.4	−2.08943	−	1.20633i	0.866025	+	1.50000i	0.910488	+	1.57701i	4.48539	+	2.20936i		−	4.17887i	−6.98737	+	0.420230i			5.25727i	−1.50000	+	2.59808i	−6.70671	−	10.0272i
19.5	−1.71634	−	0.990928i	−0.866025	−	1.50000i	−0.0361245	−	0.0625695i	4.45717	−	2.26576i			3.43267i	−2.11222	−	6.67372i			8.07061i	−1.50000	+	2.59808i	−9.89520	−	0.527928i
19.6	−1.32532	−	0.765175i	0.866025	+	1.50000i	−0.829016	−	1.43590i	−3.72620	+	3.33398i		−	2.65064i	6.34933	+	2.94719i			8.65876i	−1.50000	+	2.59808i	7.48949	−	1.56739i
19.7	−0.952353	−	0.549841i	0.866025	+	1.50000i	−1.39535	−	2.41681i	−2.62055	−	4.25825i		−	1.90471i	−6.08554	+	3.45923i			7.46761i	−1.50000	+	2.59808i	0.154330	+	5.49625i
19.8	−0.428040	−	0.247129i	−0.866025	−	1.50000i	−1.87785	−	3.25254i	−2.75389	+	4.17326i			0.856079i	−5.82770	+	3.87787i			3.83332i	−1.50000	+	2.59808i	2.21011	−	1.10575i
19.9	0.428040	+	0.247129i	0.866025	+	1.50000i	−1.87785	−	3.25254i	2.23720	−	4.47157i			0.856079i	5.82770	−	3.87787i		−	3.83332i	−1.50000	+	2.59808i	2.06266	−	1.36113i
19.10	0.952353	+	0.549841i	−0.866025	−	1.50000i	−1.39535	−	2.41681i	−4.99803	−	0.140341i		−	1.90471i	6.08554	−	3.45923i		−	7.46761i	−1.50000	+	2.59808i	−4.68273	−	2.88178i
19.11	1.32532	+	0.765175i	−0.866025	−	1.50000i	−0.829016	−	1.43590i	1.02421	−	4.89398i		−	2.65064i	−6.34933	−	2.94719i		−	8.65876i	−1.50000	+	2.59808i	5.10215	−	5.70239i
19.12	1.71634	+	0.990928i	0.866025	+	1.50000i	−0.0361245	−	0.0625695i	0.266380	+	4.99290i			3.43267i	2.11222	+	6.67372i		−	8.07061i	−1.50000	+	2.59808i	−4.49040	+	8.83346i
19.13	2.08943	+	1.20633i	−0.866025	−	1.50000i	0.910488	+	1.57701i	4.15605	+	2.77979i		−	4.17887i	6.98737	−	0.420230i		−	5.25727i	−1.50000	+	2.59808i	5.33045	+	10.8218i
19.14	2.53945	+	1.46615i	0.866025	+	1.50000i	2.29920	+	3.98234i	4.74629	−	1.57250i			5.07890i	−6.93149	−	0.976973i			1.75471i	−1.50000	+	2.59808i	14.3585	+	2.96550i
19.15	2.95153	+	1.70407i	0.866025	+	1.50000i	3.80769	+	6.59511i	−4.81594	−	1.34415i			5.90306i	5.14807	−	4.74314i			12.3217i	−1.50000	+	2.59808i	−11.9239	−	12.1740i
19.16	3.26825	+	1.88692i	−0.866025	−	1.50000i	5.12097	+	8.86977i	0.907258	−	4.91700i		−	6.53650i	1.16497	+	6.90238i			23.5561i	−1.50000	+	2.59808i	12.2431	−	14.3580i
94.1	−3.26825	+	1.88692i	0.866025	−	1.50000i	5.12097	−	8.86977i	−3.80462	−	3.24421i			6.53650i	−1.16497	+	6.90238i			23.5561i	−1.50000	−	2.59808i	18.5560	+	3.42385i
94.2	−2.95153	+	1.70407i	−0.866025	+	1.50000i	3.80769	−	6.59511i	−3.57204	+	3.49865i		−	5.90306i	−5.14807	−	4.74314i			12.3217i	−1.50000	−	2.59808i	4.58104	−	16.4134i
94.3	−2.53945	+	1.46615i	−0.866025	+	1.50000i	2.29920	−	3.98234i	1.01132	−	4.89665i		−	5.07890i	6.93149	−	0.976973i			1.75471i	−1.50000	−	2.59808i	4.61104	+	13.9176i
94.4	−2.08943	+	1.20633i	0.866025	−	1.50000i	0.910488	−	1.57701i	4.48539	−	2.20936i			4.17887i	−6.98737	−	0.420230i		−	5.25727i	−1.50000	−	2.59808i	−6.70671	+	10.0272i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
7.d	odd	6	1	inner
35.i	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	105.3.r.a	✓	32
3.b	odd	2	1		315.3.bi.e		32
5.b	even	2	1	inner	105.3.r.a	✓	32
5.c	odd	4	1		525.3.o.p		16
5.c	odd	4	1		525.3.o.q		16
7.c	even	3	1		735.3.e.a		32
7.d	odd	6	1	inner	105.3.r.a	✓	32
7.d	odd	6	1		735.3.e.a		32
15.d	odd	2	1		315.3.bi.e		32
21.g	even	6	1		315.3.bi.e		32
35.i	odd	6	1	inner	105.3.r.a	✓	32
35.i	odd	6	1		735.3.e.a		32
35.j	even	6	1		735.3.e.a		32
35.k	even	12	1		525.3.o.p		16
35.k	even	12	1		525.3.o.q		16
105.p	even	6	1		315.3.bi.e		32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
105.3.r.a	✓	32	1.a	even	1	1	trivial
105.3.r.a	✓	32	5.b	even	2	1	inner
105.3.r.a	✓	32	7.d	odd	6	1	inner
105.3.r.a	✓	32	35.i	odd	6	1	inner
315.3.bi.e		32	3.b	odd	2	1
315.3.bi.e		32	15.d	odd	2	1
315.3.bi.e		32	21.g	even	6	1
315.3.bi.e		32	105.p	even	6	1
525.3.o.p		16	5.c	odd	4	1
525.3.o.p		16	35.k	even	12	1
525.3.o.q		16	5.c	odd	4	1
525.3.o.q		16	35.k	even	12	1
735.3.e.a		32	7.c	even	3	1
735.3.e.a		32	7.d	odd	6	1
735.3.e.a		32	35.i	odd	6	1
735.3.e.a		32	35.j	even	6	1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(105, [\chi])\).