Newform orbit 124.5.o.a

• Label: 124.5.o.a
• Level: $124$
• Weight: $5$
• Character orbit: 124.o
• Analytic conductor: $12.818$
• Analytic rank: $0$
• Dimension: $88$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	124.o (of order \(30\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(12.8178754224\)
Analytic rank:	\(0\)
Dimension:	\(88\)
Relative dimension:	\(11\) over \(\Q(\zeta_{30})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
13.1		0		−7.03588	−	15.8028i		0		11.6814	+	20.2328i		0		−44.3877	−	49.2975i		0		−146.027	+	162.179i		0
13.2		0		−4.27952	−	9.61195i		0		3.43229	+	5.94490i		0		43.1077	+	47.8760i		0		−19.8758	+	22.0743i		0
13.3		0		−3.80107	−	8.53733i		0		−24.2686	−	42.0344i		0		−45.8945	−	50.9710i		0		−4.23837	+	4.70719i		0
13.4		0		−3.55268	−	7.97945i		0		−12.5017	−	21.6535i		0		17.4290	+	19.3568i		0		3.14955	−	3.49793i		0
13.5		0		−2.05606	−	4.61799i		0		6.14252	+	10.6392i		0		−13.6062	−	15.1112i		0		37.1012	−	41.2050i		0
13.6		0		1.38100	+	3.10178i		0		21.1680	+	36.6640i		0		12.2350	+	13.5884i		0		46.4857	−	51.6276i		0
13.7		0		1.72821	+	3.88162i		0		7.33763	+	12.7091i		0		−56.6769	−	62.9461i		0		42.1193	−	46.7783i		0
13.8		0		2.78469	+	6.25452i		0		−8.17325	−	14.1565i		0		16.4871	+	18.3107i		0		22.8350	−	25.3609i		0
13.9		0		3.39298	+	7.62076i		0		−15.4750	−	26.8035i		0		11.7917	+	13.0960i		0		7.63586	−	8.48048i		0
13.10		0		6.41385	+	14.4058i		0		12.5721	+	21.7754i		0		47.7518	+	53.0337i		0		−112.189	+	124.598i		0
13.11		0		6.77929	+	15.2265i		0		−2.22895	−	3.86066i		0		−53.4498	−	59.3620i		0		−131.689	+	146.256i		0
17.1		0		−11.7991	−	10.6240i		0		−0.510945	+	0.884982i		0		−6.63263	+	63.1052i		0		17.8835	+	170.150i		0
17.2		0		−8.97256	−	8.07893i		0		−1.91809	+	3.32223i		0		7.45792	−	70.9574i		0		6.77094	+	64.4212i		0
17.3		0		−5.42475	−	4.88447i		0		22.7477	−	39.4001i		0		0.180678	−	1.71904i		0		−2.89691	−	27.5623i		0
17.4		0		−3.98717	−	3.59007i		0		−24.6255	+	42.6526i		0		3.33835	−	31.7622i		0		−5.45784	−	51.9279i		0
17.5		0		−3.07010	−	2.76433i		0		−0.342480	+	0.593193i		0		−3.29625	+	31.3617i		0		−6.68282	−	63.5828i		0
17.6		0		1.30013	+	1.17065i		0		−13.3049	+	23.0447i		0		−8.54338	+	81.2848i		0		−8.14687	−	77.5123i		0
17.7		0		3.32625	+	2.99497i		0		10.0265	−	17.3665i		0		0.840912	−	8.00074i		0		−6.37270	−	60.6322i		0
17.8		0		6.29564	+	5.66862i		0		−3.44300	+	5.96345i		0		−1.27725	+	12.1523i		0		−0.964961	−	9.18099i		0
17.9		0		6.45809	+	5.81489i		0		4.44246	−	7.69456i		0		6.90219	−	65.6700i		0		−0.572828	−	5.45009i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
31.h	odd	30	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	124.5.o.a	✓	88
31.h	odd	30	1	inner	124.5.o.a	✓	88

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
124.5.o.a	✓	88	1.a	even	1	1	trivial
124.5.o.a	✓	88	31.h	odd	30	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(124, [\chi])\).