Newform orbit 115.5.i.a

• Label: 115.5.i.a
• Level: $115$
• Weight: $5$
• Character orbit: 115.i
• Analytic conductor: $11.888$
• Analytic rank: $0$
• Dimension: $460$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	115.i (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(11.8875457546\)
Analytic rank:	\(0\)
Dimension:	\(460\)
Relative dimension:	\(46\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 460 q + 306 q^{4} - 11 q^{5} - 182 q^{6} + 944 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
14.1	−2.18300	−	7.43463i	−2.64484	+	2.29177i	−37.0481	+	23.8094i	−13.3410	−	21.1428i	22.8121	+	14.6605i	−5.36934	+	11.7572i	164.196	+	142.276i	−9.78452	+	68.0528i	−128.066	+	145.340i
14.2	−2.10144	−	7.15685i	10.8466	−	9.39863i	−33.3445	+	21.4292i	23.7360	−	7.84872i	−90.0581	−	57.8768i	32.6308	−	71.4516i	133.243	+	115.456i	17.7869	−	123.711i	−106.052	−	153.381i
14.3	−2.01699	−	6.86925i	−6.92280	+	5.99864i	−29.6583	+	19.0602i	3.87662	+	24.6976i	55.1695	+	35.4553i	37.5707	−	82.2683i	104.181	+	90.2729i	0.413989	−	2.87936i	161.835	−	76.4444i
14.4	−1.98199	−	6.75004i	5.91077	−	5.12171i	−28.1747	+	18.1068i	−0.890702	+	24.9841i	−46.2868	−	29.7467i	−18.3089	+	40.0910i	92.9960	+	80.5815i	−2.82222	+	19.6290i	170.409	−	43.5060i
14.5	−1.80372	−	6.14291i	−12.3789	+	10.7264i	−21.0219	+	13.5100i	−20.7399	+	13.9592i	88.2193	+	56.6951i	−35.9524	+	78.7248i	43.4924	+	37.6864i	26.6544	−	185.386i	123.159	+	102.225i
14.6	−1.77123	−	6.03227i	11.0627	−	9.58586i	−19.7910	+	12.7189i	−22.7723	−	10.3161i	−77.4191	−	49.7542i	−22.6376	+	49.5694i	35.7565	+	30.9832i	18.9665	−	131.915i	−21.8945	+	155.641i
14.7	−1.75464	−	5.97575i	−7.06070	+	6.11814i	−19.1708	+	12.3203i	24.2582	+	6.04485i	48.9494	+	31.4579i	−12.9566	+	28.3710i	31.9516	+	27.6862i	0.894466	−	6.22115i	−6.44183	−	155.567i
14.8	−1.72741	−	5.88302i	−0.556901	+	0.482558i	−18.1659	+	11.6745i	22.6244	−	10.6365i	3.80090	+	2.44269i	−11.9218	+	26.1051i	25.9210	+	22.4607i	−11.4502	+	79.6381i	−101.657	−	114.726i
14.9	−1.60185	−	5.45541i	6.57117	−	5.69395i	−13.7355	+	8.82725i	−24.7386	+	3.60566i	−41.5888	−	26.7275i	31.2269	−	68.3774i	1.40679	+	1.21899i	−0.768314	+	5.34374i	59.2979	+	129.183i
14.10	−1.49289	−	5.08433i	−10.7675	+	9.33009i	−10.1616	+	6.53048i	−3.03564	−	24.8150i	63.5120	+	40.8167i	25.1721	−	55.1192i	−15.7018	−	13.6057i	17.3609	−	120.748i	−121.636	+	52.4804i
14.11	−1.34542	−	4.58206i	4.34914	−	3.76855i	−5.72511	+	3.67931i	4.19085	−	24.6462i	−23.1191	−	14.8578i	7.38910	−	16.1799i	−33.1839	−	28.7540i	−6.81447	+	47.3957i	−118.569	+	13.9567i
14.12	−1.33057	−	4.53150i	−3.81868	+	3.30890i	−5.30401	+	3.40868i	−24.7617	+	3.44348i	20.0753	+	12.9016i	3.15920	−	6.91768i	−34.6044	−	29.9848i	−7.89404	+	54.9042i	48.5512	+	107.626i
14.13	−1.13341	−	3.86005i	2.81764	−	2.44150i	−0.155323	+	0.0998199i	1.67039	+	24.9441i	−12.6179	−	8.10901i	−7.78355	+	17.0436i	−48.0849	−	41.6658i	−9.54933	+	66.4170i	94.3924	−	34.7198i
14.14	−1.04916	−	3.57310i	12.0617	−	10.4515i	1.79375	−	1.15277i	24.8811	−	2.43500i	−49.9988	−	32.1323i	−30.9341	+	67.7361i	−51.0308	−	44.2185i	24.7226	−	171.949i	−34.8047	−	86.3480i
14.15	−0.944999	−	3.21837i	6.93728	−	6.01119i	3.99518	−	2.56754i	17.7521	+	17.6030i	−25.9019	−	16.6462i	19.4786	−	42.6523i	−52.5982	−	45.5766i	0.463978	−	3.22704i	39.8771	−	73.7675i
14.16	−0.742368	−	2.52827i	−9.67129	+	8.38022i	7.61900	−	4.89643i	19.4722	+	15.6790i	28.3671	+	18.2305i	8.49240	−	18.5958i	−49.8982	−	43.2370i	11.7782	−	81.9194i	25.1853	−	60.8708i
14.17	−0.674293	−	2.29643i	0.167586	−	0.145214i	8.64114	−	5.55332i	−14.8202	−	20.1336i	−0.446476	−	0.286933i	−39.0504	+	85.5085i	−47.5202	−	41.1765i	−11.5205	+	80.1269i	−36.2423	+	47.6095i
14.18	−0.639671	−	2.17852i	−10.2600	+	8.89037i	9.12329	−	5.86318i	13.0251	−	21.3388i	25.9309	+	16.6648i	−26.3066	+	57.6035i	−46.0637	−	39.9144i	14.7021	−	102.255i	−54.8189	−	14.7256i
14.19	−0.617270	−	2.10223i	−5.53313	+	4.79448i	9.42171	−	6.05496i	−12.9412	+	21.3898i	13.4945	+	8.67241i	−1.32728	+	2.90635i	−45.0380	−	39.0256i	−3.89907	+	27.1186i	52.9546	+	14.0021i
14.20	−0.488218	−	1.66272i	9.79680	−	8.48898i	10.9338	−	7.02672i	−7.35574	−	23.8934i	−18.8977	−	12.1448i	13.0669	−	28.6125i	−37.9759	−	32.9063i	12.3871	−	86.1541i	−36.1367	+	23.8957i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
23.d	odd	22	1	inner
115.i	odd	22	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	115.5.i.a	✓	460
5.b	even	2	1	inner	115.5.i.a	✓	460
23.d	odd	22	1	inner	115.5.i.a	✓	460
115.i	odd	22	1	inner	115.5.i.a	✓	460

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
115.5.i.a	✓	460	1.a	even	1	1	trivial
115.5.i.a	✓	460	5.b	even	2	1	inner
115.5.i.a	✓	460	23.d	odd	22	1	inner
115.5.i.a	✓	460	115.i	odd	22	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(115, [\chi])\).