Newform orbit 174.6.f.a

• Label: 174.6.f.a
• Level: $174$
• Weight: $6$
• Character orbit: 174.f
• Analytic conductor: $27.907$
• Analytic rank: $0$
• Dimension: $100$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 174 = 2 \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	174.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(27.9067846475\)
Analytic rank:	\(0\)
Dimension:	\(100\)
Relative dimension:	\(50\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 100 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
17.1	−2.82843	−	2.82843i	10.8506	+	11.1922i			16.0000i	−83.3299			0.966075	−	62.3463i	−151.624			45.2548	−	45.2548i	−7.52890	+	242.883i	235.693	+	235.693i
17.2	−2.82843	−	2.82843i	−9.25264	−	12.5455i			16.0000i	−87.4995			−9.31353	+	61.6543i	−12.0188			45.2548	−	45.2548i	−71.7774	+	232.157i	247.486	+	247.486i
17.3	−2.82843	−	2.82843i	15.0645	−	4.00750i			16.0000i	−70.7877			−53.9438	−	31.2740i	185.643			45.2548	−	45.2548i	210.880	−	120.742i	200.218	+	200.218i
17.4	−2.82843	−	2.82843i	−15.1167	+	3.80607i			16.0000i	−66.9953			53.5216	+	31.9912i	62.3837			45.2548	−	45.2548i	214.028	−	115.070i	189.491	+	189.491i
17.5	−2.82843	−	2.82843i	4.99445	−	14.7667i			16.0000i	−62.0112			−55.8930	+	27.6401i	113.133			45.2548	−	45.2548i	−193.111	−	147.503i	175.394	+	175.394i
17.6	−2.82843	−	2.82843i	14.6083	+	5.44034i			16.0000i	47.4498			−25.9309	−	56.7061i	195.528			45.2548	−	45.2548i	183.805	+	158.948i	−134.208	−	134.208i
17.7	−2.82843	−	2.82843i	0.267341	−	15.5862i			16.0000i	47.4311			−44.8405	+	43.3282i	−118.191			45.2548	−	45.2548i	−242.857	−	8.33364i	−134.156	−	134.156i
17.8	−2.82843	−	2.82843i	−14.0677	−	6.71564i			16.0000i	47.6338			20.7947	+	58.7842i	209.411			45.2548	−	45.2548i	152.800	+	188.947i	−134.729	−	134.729i
17.9	−2.82843	−	2.82843i	1.72490	+	15.4927i			16.0000i	40.8695			38.9413	−	48.6988i	101.200			45.2548	−	45.2548i	−237.049	+	53.4469i	−115.596	−	115.596i
17.10	−2.82843	−	2.82843i	13.6593	−	7.51157i			16.0000i	−39.7359			−59.8803	−	17.3884i	−32.7184			45.2548	−	45.2548i	130.153	−	205.206i	112.390	+	112.390i
17.11	−2.82843	−	2.82843i	−7.66785	+	13.5722i			16.0000i	−36.9732			60.0759	−	16.7000i	−232.884			45.2548	−	45.2548i	−125.408	−	208.139i	104.576	+	104.576i
17.12	−2.82843	−	2.82843i	−14.3531	−	6.08172i			16.0000i	28.1087			23.3951	+	57.7985i	−83.1287			45.2548	−	45.2548i	169.025	+	174.584i	−79.5035	−	79.5035i
17.13	−2.82843	−	2.82843i	15.5432	−	1.18663i			16.0000i	−25.4726			−47.3192	−	40.6066i	−102.049			45.2548	−	45.2548i	240.184	−	36.8881i	72.0473	+	72.0473i
17.14	−2.82843	−	2.82843i	−3.58468	+	15.1707i			16.0000i	−18.7104			53.0482	−	32.7702i	24.5071			45.2548	−	45.2548i	−217.300	−	108.764i	52.9210	+	52.9210i
17.15	−2.82843	−	2.82843i	9.52683	+	12.3385i			16.0000i	14.7905			7.95273	−	61.8446i	−3.62717			45.2548	−	45.2548i	−61.4792	+	235.094i	−41.8339	−	41.8339i
17.16	−2.82843	−	2.82843i	−8.36411	−	13.1545i			16.0000i	5.06137			−13.5493	+	60.8639i	−173.387			45.2548	−	45.2548i	−103.083	+	220.052i	−14.3157	−	14.3157i
17.17	−2.82843	−	2.82843i	−2.28871	−	15.4195i			16.0000i	2.41047			−37.1396	+	50.0864i	144.406			45.2548	−	45.2548i	−232.524	+	70.5815i	−6.81784	−	6.81784i
17.18	−2.82843	−	2.82843i	10.2926	−	11.7074i			16.0000i	31.5863			−62.2253	+	4.00169i	−96.0384			45.2548	−	45.2548i	−31.1258	−	240.998i	−89.3396	−	89.3396i
17.19	−2.82843	−	2.82843i	−14.8223	+	4.82688i			16.0000i	−60.6708			55.5763	+	28.2714i	−55.9245			45.2548	−	45.2548i	196.403	−	143.091i	171.603	+	171.603i
17.20	−2.82843	−	2.82843i	−12.5821	+	9.20272i			16.0000i	59.7952			61.6169	+	9.55839i	117.986			45.2548	−	45.2548i	73.6197	−	231.580i	−169.126	−	169.126i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
29.c	odd	4	1	inner
87.f	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	174.6.f.a	✓	100
3.b	odd	2	1	inner	174.6.f.a	✓	100
29.c	odd	4	1	inner	174.6.f.a	✓	100
87.f	even	4	1	inner	174.6.f.a	✓	100

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
174.6.f.a	✓	100	1.a	even	1	1	trivial
174.6.f.a	✓	100	3.b	odd	2	1	inner
174.6.f.a	✓	100	29.c	odd	4	1	inner
174.6.f.a	✓	100	87.f	even	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{6}^{\mathrm{new}}(174, [\chi])\).