Newform orbit 92.2.h.a

• Label: 92.2.h.a
• Level: $92$
• Weight: $2$
• Character orbit: 92.h
• Analytic conductor: $0.735$
• Analytic rank: $0$
• Dimension: $100$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	92.h (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(0.734623698596\)
Analytic rank:	\(0\)
Dimension:	\(100\)
Relative dimension:	\(10\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 100 q - 7 q^{2} - 11 q^{4} - 22 q^{5} - 12 q^{6} - 10 q^{8} - 12 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
7.1	−1.32329	+	0.498911i	−0.998425	−	1.55358i	1.50217	−	1.32041i	−3.48007	+	1.58929i	2.09630	+	1.55770i	−2.92167	+	0.857881i	−1.32904	+	2.49673i	−0.170511	+	0.373368i	3.81221	−	3.83934i
7.2	−1.29560	−	0.566948i	−0.145312	−	0.226109i	1.35714	+	1.46907i	1.05084	−	0.479903i	0.0600729	+	0.375331i	1.55538	−	0.456702i	−0.925416	−	2.67275i	1.21624	−	2.66318i	−1.63355	+	0.0259878i
7.3	−1.25282	+	0.656083i	1.27476	+	1.98356i	1.13911	−	1.64391i	2.16405	−	0.988288i	−2.89842	−	1.64870i	−2.09343	+	0.614686i	−0.348560	+	2.80687i	−1.06327	+	2.32823i	−2.06276	+	2.65794i
7.4	−0.471110	+	1.33344i	−1.27476	−	1.98356i	−1.55611	−	1.25639i	2.16405	−	0.988288i	3.24551	−	0.765333i	2.09343	−	0.614686i	2.40842	−	1.48308i	−1.06327	+	2.32823i	0.298314	+	3.35122i
7.5	−0.312716	−	1.37921i	1.44811	+	2.25330i	−1.80442	+	0.862599i	0.189929	−	0.0867378i	2.65492	−	2.70189i	2.09970	−	0.616528i	1.75397	+	2.21892i	−1.73411	+	3.79717i	−0.179023	−	0.234827i
7.6	−0.305510	+	1.38082i	0.998425	+	1.55358i	−1.81333	−	0.843709i	−3.48007	+	1.58929i	−2.45024	+	0.904011i	2.92167	−	0.857881i	1.71900	−	2.24612i	−0.170511	+	0.373368i	−1.13133	−	5.29089i
7.7	0.550867	−	1.30252i	−0.874133	−	1.36018i	−1.39309	−	1.43503i	−1.57961	+	0.721385i	−2.25318	+	0.389295i	3.24497	−	0.952810i	−2.63655	+	1.02401i	0.160270	−	0.350942i	0.0694584	+	2.45486i
7.8	0.745560	+	1.20172i	0.145312	+	0.226109i	−0.888280	+	1.79191i	1.05084	−	0.479903i	−0.163382	+	0.343203i	−1.55538	+	0.456702i	−2.81565	+	0.268514i	1.21624	−	2.66318i	1.36018	+	0.905024i
7.9	1.21086	−	0.730627i	0.874133	+	1.36018i	0.932368	−	1.76938i	−1.57961	+	0.721385i	2.05224	+	1.00832i	−3.24497	+	0.952810i	−0.163786	−	2.82368i	0.160270	−	0.350942i	−1.38563	+	2.02761i
7.10	1.40967	+	0.113251i	−1.44811	−	2.25330i	1.97435	+	0.319294i	0.189929	−	0.0867378i	−1.78617	−	3.34042i	−2.09970	+	0.616528i	2.74702	+	0.673698i	−1.73411	+	3.79717i	0.277561	−	0.100762i
11.1	−1.39348	+	0.241286i	2.01686	+	0.289980i	1.88356	−	0.672454i	−0.680282	−	2.31683i	−2.88042	+	0.0825585i	0.800569	+	0.923906i	−2.46245	+	1.39153i	1.10515	+	0.324501i	1.50698	+	3.06431i
11.2	−1.35313	−	0.411128i	−2.71502	−	0.390360i	1.66195	+	1.11262i	0.232350	+	0.791311i	3.51329	+	1.64443i	2.90308	+	3.35033i	−1.79141	−	2.18880i	4.34045	+	1.27447i	0.0109292	−	1.16628i
11.3	−1.04738	−	0.950264i	1.65123	+	0.237411i	0.193997	+	1.99057i	0.934364	+	3.18215i	−1.50386	−	1.81776i	−0.148303	−	0.171151i	1.68838	−	2.26922i	−0.208284	−	0.0611576i	2.04525	−	4.22080i
11.4	−0.798353	+	1.16732i	−2.01686	−	0.289980i	−0.725264	−	1.86386i	−0.680282	−	2.31683i	1.94866	−	2.12281i	−0.800569	−	0.923906i	2.75474	+	0.641408i	1.10515	+	0.324501i	3.24758	+	1.05554i
11.5	−0.665666	−	1.24775i	−0.837775	−	0.120454i	−1.11378	+	1.66117i	−0.870000	−	2.96295i	0.407382	+	1.12552i	−2.18927	−	2.52655i	2.81414	+	0.283931i	−2.19112	−	0.643371i	−3.11790	+	3.05788i
11.6	−0.188138	+	1.40164i	2.71502	+	0.390360i	−1.92921	−	0.527404i	0.232350	+	0.791311i	−1.05794	+	3.73204i	−2.90308	−	3.35033i	1.10219	−	2.60484i	4.34045	+	1.27447i	−1.15285	+	0.176796i
11.7	0.429294	+	1.34748i	−1.65123	−	0.237411i	−1.63141	+	1.15693i	0.934364	+	3.18215i	−0.388957	−	2.32692i	0.148303	+	0.171151i	−2.25930	−	1.70163i	−0.208284	−	0.0611576i	−3.88677	+	2.62512i
11.8	0.630624	−	1.26582i	0.942266	+	0.135477i	−1.20463	−	1.59652i	0.224821	+	0.765671i	0.765707	−	1.10731i	0.326270	+	0.376536i	−2.78058	+	0.518040i	−2.00897	−	0.589886i	1.11098	+	0.198266i
11.9	0.858469	+	1.12385i	0.837775	+	0.120454i	−0.526063	+	1.92957i	−0.870000	−	2.96295i	0.583832	+	1.04494i	2.18927	+	2.52655i	−2.62015	+	1.06526i	−2.19112	−	0.643371i	2.58303	−	3.52134i
11.10	1.41341	−	0.0477935i	−0.942266	−	0.135477i	1.99543	−	0.135103i	0.224821	+	0.765671i	−1.33828	−	0.146450i	−0.326270	−	0.376536i	2.81390	−	0.286325i	−2.00897	−	0.589886i	0.354358	+	1.07146i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
23.d	odd	22	1	inner
92.h	even	22	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	92.2.h.a	✓	100
3.b	odd	2	1		828.2.u.a		100
4.b	odd	2	1	inner	92.2.h.a	✓	100
12.b	even	2	1		828.2.u.a		100
23.d	odd	22	1	inner	92.2.h.a	✓	100
69.g	even	22	1		828.2.u.a		100
92.h	even	22	1	inner	92.2.h.a	✓	100
276.j	odd	22	1		828.2.u.a		100

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
92.2.h.a	✓	100	1.a	even	1	1	trivial
92.2.h.a	✓	100	4.b	odd	2	1	inner
92.2.h.a	✓	100	23.d	odd	22	1	inner
92.2.h.a	✓	100	92.h	even	22	1	inner
828.2.u.a		100	3.b	odd	2	1
828.2.u.a		100	12.b	even	2	1
828.2.u.a		100	69.g	even	22	1
828.2.u.a		100	276.j	odd	22	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(92, [\chi])\).