Newform orbit 115.2.j.a

• Label: 115.2.j.a
• Level: $115$
• Weight: $2$
• Character orbit: 115.j
• Analytic conductor: $0.918$
• Analytic rank: $0$
• Dimension: $100$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.j (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(0.918279623245\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 100 q - 14 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
4.1	−2.04322	+	0.933106i	0.0755218	+	0.257204i	1.99433	−	2.30158i	0.256006	−	2.22136i	−0.394306	−	0.455053i	0.783997	−	0.112722i	−0.661572	+	2.25311i	2.46331	−	1.58307i	1.54969	+	4.77761i
4.2	−1.55935	+	0.712130i	−0.478796	−	1.63063i	0.614711	−	0.709414i	−1.26571	+	1.84336i	1.90783	+	2.20175i	4.84873	−	0.697142i	0.512574	−	1.74567i	0.0940571	−	0.0604468i	0.660971	−	3.77579i
4.3	−1.49755	+	0.683908i	0.900592	+	3.06714i	0.465201	−	0.536871i	2.15615	+	0.592474i	−3.44632	−	3.97726i	0.632042	−	0.0908739i	0.598154	−	2.03713i	−6.07249	+	3.90255i	−3.63413	+	0.587347i
4.4	−0.477984	+	0.218288i	−0.663307	−	2.25902i	−1.12890	+	1.30282i	−1.43085	−	1.71833i	0.810167	+	0.934983i	−3.03882	+	0.436916i	0.551291	−	1.87752i	−2.13942	+	1.37492i	1.05902	+	0.508999i
4.5	−0.175347	+	0.0800783i	0.167074	+	0.569000i	−1.28539	+	1.48342i	0.481985	+	2.18350i	−0.0748604	−	0.0863935i	−3.28793	+	0.472733i	0.215217	−	0.732961i	2.22791	−	1.43179i	−0.259366	−	0.344274i
4.6	0.175347	−	0.0800783i	−0.167074	−	0.569000i	−1.28539	+	1.48342i	2.18641	−	0.468631i	−0.0748604	−	0.0863935i	3.28793	−	0.472733i	−0.215217	+	0.732961i	2.22791	−	1.43179i	0.345853	−	0.257257i
4.7	0.477984	−	0.218288i	0.663307	+	2.25902i	−1.12890	+	1.30282i	−2.15745	−	0.587726i	0.810167	+	0.934983i	3.03882	−	0.436916i	−0.551291	+	1.87752i	−2.13942	+	1.37492i	−1.15952	+	0.190022i
4.8	1.49755	−	0.683908i	−0.900592	−	3.06714i	0.465201	−	0.536871i	1.43463	+	1.71518i	−3.44632	−	3.97726i	−0.632042	+	0.0908739i	−0.598154	+	2.03713i	−6.07249	+	3.90255i	3.32145	+	1.58741i
4.9	1.55935	−	0.712130i	0.478796	+	1.63063i	0.614711	−	0.709414i	1.15098	−	1.91709i	1.90783	+	2.20175i	−4.84873	+	0.697142i	−0.512574	+	1.74567i	0.0940571	−	0.0604468i	0.429565	−	3.80906i
4.10	2.04322	−	0.933106i	−0.0755218	−	0.257204i	1.99433	−	2.30158i	−1.91428	+	1.15566i	−0.394306	−	0.455053i	−0.783997	+	0.112722i	0.661572	−	2.25311i	2.46331	−	1.58307i	−2.83293	+	4.14748i
9.1	−0.743795	−	2.53313i	−1.34601	+	1.16633i	−4.18102	+	2.68698i	−2.23607	+	0.00123367i	3.95561	+	2.54212i	1.87277	+	0.855264i	5.92582	+	5.13475i	0.0244873	−	0.170313i	1.66630	+	5.66334i
9.2	−0.651256	−	2.21797i	0.917405	−	0.794936i	−2.81277	+	1.80765i	1.79096	−	1.33883i	−2.36061	−	1.51707i	−1.70619	−	0.779189i	2.34716	+	2.03383i	−0.217236	+	1.51091i	−4.13586	−	3.10038i
9.3	−0.394732	−	1.34433i	−1.97191	+	1.70867i	0.0310904	−	0.0199806i	2.16612	+	0.554912i	3.07540	+	1.97644i	2.68179	+	1.22473i	−2.15687	−	1.86894i	0.541936	−	3.76925i	−0.109049	−	3.13103i
9.4	−0.320885	−	1.09283i	1.24484	−	1.07866i	0.591189	−	0.379934i	0.429235	+	2.19448i	−1.57825	−	1.01428i	1.40950	+	0.643697i	−2.32646	−	2.01589i	−0.0408222	+	0.283925i	2.26047	−	1.17326i
9.5	−0.176688	−	0.601743i	0.563711	−	0.488459i	1.35163	−	0.868641i	−1.82300	−	1.29486i	−0.393527	−	0.252905i	0.620531	+	0.283387i	−1.70945	−	1.48124i	−0.347766	+	2.41877i	−0.457073	+	1.32576i
9.6	0.176688	+	0.601743i	−0.563711	+	0.488459i	1.35163	−	0.868641i	1.38435	−	1.75601i	−0.393527	−	0.252905i	−0.620531	−	0.283387i	1.70945	+	1.48124i	−0.347766	+	2.41877i	1.30126	+	0.522758i
9.7	0.320885	+	1.09283i	−1.24484	+	1.07866i	0.591189	−	0.379934i	0.206409	+	2.22652i	−1.57825	−	1.01428i	−1.40950	−	0.643697i	2.32646	+	2.01589i	−0.0408222	+	0.283925i	−2.36698	+	0.940028i
9.8	0.394732	+	1.34433i	1.97191	−	1.70867i	0.0310904	−	0.0199806i	−1.92204	+	1.14270i	3.07540	+	1.97644i	−2.68179	−	1.22473i	2.15687	+	1.86894i	0.541936	−	3.76925i	−2.29486	−	2.13280i
9.9	0.651256	+	2.21797i	−0.917405	+	0.794936i	−2.81277	+	1.80765i	−2.09560	−	0.780027i	−2.36061	−	1.51707i	1.70619	+	0.779189i	−2.34716	−	2.03383i	−0.217236	+	1.51091i	0.365306	−	5.15599i
9.10	0.743795	+	2.53313i	1.34601	−	1.16633i	−4.18102	+	2.68698i	2.14584	−	0.628789i	3.95561	+	2.54212i	−1.87277	−	0.855264i	−5.92582	−	5.13475i	0.0244873	−	0.170313i	3.18887	+	4.96800i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
23.c	even	11	1	inner
115.j	even	22	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	115.2.j.a	✓	100
5.b	even	2	1	inner	115.2.j.a	✓	100
5.c	odd	4	2		575.2.k.g		100
23.c	even	11	1	inner	115.2.j.a	✓	100
115.j	even	22	1	inner	115.2.j.a	✓	100
115.k	odd	44	2		575.2.k.g		100

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
115.2.j.a	✓	100	1.a	even	1	1	trivial
115.2.j.a	✓	100	5.b	even	2	1	inner
115.2.j.a	✓	100	23.c	even	11	1	inner
115.2.j.a	✓	100	115.j	even	22	1	inner
575.2.k.g		100	5.c	odd	4	2
575.2.k.g		100	115.k	odd	44	2

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(115, [\chi])\).