Newform orbit 232.2.v.a

• Label: 232.2.v.a
• Level: $232$
• Weight: $2$
• Character orbit: 232.v
• Analytic conductor: $1.853$
• Analytic rank: $0$
• Dimension: $336$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 232 = 2^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	232.v (of order \(28\), degree \(12\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.85252932689\)
Analytic rank:	\(0\)
Dimension:	\(336\)
Relative dimension:	\(28\) over \(\Q(\zeta_{28})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 336 q - 14 q^{2} - 24 q^{3} - 14 q^{4} - 14 q^{6} - 8 q^{8} - 28 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3.1	−1.41414	+	0.0147370i	−1.16011	+	0.405941i	1.99957	−	0.0416802i	0.839613	+	3.67859i	1.63458	−	0.591153i	1.19699	−	2.48557i	−2.82705	+	0.0884090i	−1.16442	+	0.928595i	−1.24154	−	5.18965i
3.2	−1.41262	−	0.0671653i	2.72856	−	0.954763i	1.99098	+	0.189758i	−0.427278	−	1.87203i	−3.91853	+	1.16545i	0.436790	−	0.907003i	−2.79975	−	0.401780i	4.18795	−	3.33978i	0.477845	+	2.67316i
3.3	−1.41128	+	0.0909979i	−2.21981	+	0.776744i	1.98344	−	0.256847i	−0.273633	−	1.19887i	3.06209	−	1.29820i	−1.25786	+	2.61197i	−2.77582	+	0.542973i	1.97872	−	1.57797i	0.495268	+	1.66704i
3.4	−1.25244	−	0.656815i	0.446512	−	0.156241i	1.13719	+	1.64524i	−0.347189	−	1.52113i	−0.661848	−	0.0975935i	1.04507	−	2.17011i	−0.343639	−	2.80747i	−2.17053	+	1.73094i	−0.564272	+	2.13316i
3.5	−1.24857	+	0.664135i	1.91827	−	0.671232i	1.11785	−	1.65844i	0.529151	+	2.31836i	−1.94930	+	2.11207i	−0.865231	+	1.79667i	−0.294285	+	2.81308i	0.883712	−	0.704736i	−2.20039	−	2.54321i
3.6	−1.13518	−	0.843424i	0.446512	−	0.156241i	0.577272	+	1.91488i	0.347189	+	1.52113i	−0.638649	−	0.199237i	−1.04507	+	2.17011i	0.959745	−	2.66062i	−2.17053	+	1.73094i	0.888838	−	2.01959i
3.7	−0.871189	+	1.11401i	−2.43003	+	0.850303i	−0.482058	−	1.94104i	−0.196274	−	0.859931i	1.16976	−	3.44786i	0.941178	−	1.95438i	2.58231	+	1.15399i	2.83652	−	2.26205i	1.12897	+	0.530511i
3.8	−0.866991	+	1.11729i	−0.731900	+	0.256103i	−0.496653	−	1.93735i	0.231246	+	1.01316i	0.348411	−	1.03978i	−0.988635	+	2.05292i	2.59517	+	1.12476i	−1.87541	+	1.49559i	−1.33247	−	0.620029i
3.9	−0.674058	+	1.24324i	1.73678	−	0.607725i	−1.09129	−	1.67603i	−0.936652	−	4.10374i	−0.415142	+	2.56888i	−1.12340	+	2.33276i	2.81930	−	0.226992i	0.301579	−	0.240501i	5.73329	+	1.60168i
3.10	−0.673426	−	1.24358i	2.72856	−	0.954763i	−1.09300	+	1.67492i	0.427278	+	1.87203i	−3.02481	−	2.75022i	−0.436790	+	0.907003i	2.81895	+	0.231296i	4.18795	−	3.33978i	2.04028	−	1.79203i
3.11	−0.600293	−	1.28049i	−1.16011	+	0.405941i	−1.27930	+	1.53734i	−0.839613	−	3.67859i	1.21621	+	1.24183i	−1.19699	+	2.48557i	2.73649	+	0.715269i	−1.16442	+	0.928595i	−4.20637	+	3.28334i
3.12	−0.530346	−	1.31100i	−2.21981	+	0.776744i	−1.43747	+	1.39057i	0.273633	+	1.19887i	2.19558	+	2.49823i	1.25786	−	2.61197i	2.58540	+	1.14704i	1.97872	−	1.57797i	1.42660	−	0.994548i
3.13	−0.391162	+	1.35904i	2.27761	−	0.796969i	−1.69398	−	1.06321i	0.198708	+	0.870599i	0.192200	+	3.40710i	2.09720	−	4.35488i	2.10757	−	1.88631i	2.20684	−	1.75989i	−1.26091	−	0.0704923i
3.14	0.0566313	−	1.41308i	1.91827	−	0.671232i	−1.99359	−	0.160049i	−0.529151	−	2.31836i	−0.839869	−	2.74868i	0.865231	−	1.79667i	−0.339061	+	2.80803i	0.883712	−	0.704736i	−3.30599	+	0.616440i
3.15	0.0591354	+	1.41298i	0.130272	−	0.0455843i	−1.99301	+	0.167114i	0.242922	+	1.06431i	0.0721133	+	0.181376i	−0.896926	+	1.86249i	−0.353985	−	2.80619i	−2.33060	+	1.85859i	−1.48948	+	0.406181i
3.16	0.291156	+	1.38392i	−1.09940	+	0.384697i	−1.83046	+	0.805873i	−0.809398	−	3.54621i	−0.852486	−	1.40947i	1.89455	−	3.93408i	−1.64821	−	2.29856i	−1.28481	+	1.02460i	4.67200	−	2.15264i
3.17	0.442196	+	1.34330i	−3.14423	+	1.10021i	−1.60893	+	1.18801i	0.757049	+	3.31685i	−2.86829	−	3.73715i	−0.134366	+	0.279013i	−2.30731	−	1.63594i	6.33023	−	5.04819i	−4.12077	+	2.48364i
3.18	0.625698	−	1.26827i	−2.43003	+	0.850303i	−1.21700	−	1.58710i	0.196274	+	0.859931i	−0.442051	+	3.61396i	−0.941178	+	1.95438i	−2.77435	+	0.550439i	2.83652	−	2.26205i	1.21343	+	0.289130i
3.19	0.630466	−	1.26590i	−0.731900	+	0.256103i	−1.20503	−	1.59622i	−0.231246	−	1.01316i	−0.137236	+	1.08798i	0.988635	−	2.05292i	−2.78039	+	0.519085i	−1.87541	+	1.49559i	−1.42835	−	0.346025i
3.20	0.827657	−	1.14673i	1.73678	−	0.607725i	−0.629966	−	1.89819i	0.936652	+	4.10374i	0.740563	−	2.49460i	1.12340	−	2.33276i	−2.69811	−	0.848655i	0.301579	−	0.240501i	5.48110	+	2.32241i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
8.d	odd	2	1	inner
29.f	odd	28	1	inner
232.v	even	28	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	232.2.v.a	✓	336
4.b	odd	2	1		928.2.bn.a		336
8.b	even	2	1		928.2.bn.a		336
8.d	odd	2	1	inner	232.2.v.a	✓	336
29.f	odd	28	1	inner	232.2.v.a	✓	336
116.l	even	28	1		928.2.bn.a		336
232.u	odd	28	1		928.2.bn.a		336
232.v	even	28	1	inner	232.2.v.a	✓	336

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
232.2.v.a	✓	336	1.a	even	1	1	trivial
232.2.v.a	✓	336	8.d	odd	2	1	inner
232.2.v.a	✓	336	29.f	odd	28	1	inner
232.2.v.a	✓	336	232.v	even	28	1	inner
928.2.bn.a		336	4.b	odd	2	1
928.2.bn.a		336	8.b	even	2	1
928.2.bn.a		336	116.l	even	28	1
928.2.bn.a		336	232.u	odd	28	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(232, [\chi])\).