Newform orbit 725.2.bh.a

• Label: 725.2.bh.a
• Level: $725$
• Weight: $2$
• Character orbit: 725.bh
• Analytic conductor: $5.789$
• Analytic rank: $0$
• Dimension: $1728$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.bh (of order \(70\), degree \(24\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.78915414654\)
Analytic rank:	\(0\)
Dimension:	\(1728\)
Relative dimension:	\(72\) over \(\Q(\zeta_{70})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{70}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) 1728 * q - 35 * q^2 - 35 * q^3 + 53 * q^4 - 16 * q^5 - 19 * q^6 - 35 * q^8 + 49 * q^9 - 28 * q^10 - 21 * q^11 - 25 * q^13 - 21 * q^14 - 42 * q^15 + 37 * q^16 - 21 * q^19 + 54 * q^20 - 21 * q^21 - 25 * q^22 - 45 * q^23 - 68 * q^24 + 4 * q^25 - 14 * q^26 - 140 * q^27 - 40 * q^28 - 4 * q^29 - 154 * q^30 - 21 * q^31 - 5 * q^33 + 104 * q^34 - 50 * q^35 + 59 * q^36 - 35 * q^37 - 200 * q^38 - 21 * q^39 - 91 * q^40 - 65 * q^42 - 21 * q^44 - 114 * q^45 - 35 * q^47 - 35 * q^48 + 144 * q^49 + 196 * q^50 - 54 * q^51 + 180 * q^52 - 155 * q^53 - 25 * q^54 - 84 * q^55 - 49 * q^56 + 365 * q^58 - 204 * q^59 - 259 * q^60 - 105 * q^61 - 25 * q^62 - 95 * q^63 + 73 * q^64 - 22 * q^65 - 21 * q^66 + 15 * q^67 - 21 * q^69 + 58 * q^71 - 35 * q^72 - 35 * q^73 - 128 * q^74 - 168 * q^76 - 35 * q^77 + 165 * q^78 - 21 * q^79 - 377 * q^80 - 67 * q^81 - 25 * q^83 + 42 * q^84 + 77 * q^85 - 324 * q^86 + 285 * q^87 + 120 * q^88 - 21 * q^89 + 21 * q^90 + 37 * q^91 - 165 * q^92 - 77 * q^94 + 84 * q^95 + 313 * q^96 - 35 * q^97 - 315 * q^98

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	−2.33360	−	1.39426i	0.138522	+	0.0251381i	2.55400	+	4.74613i	1.98321	+	1.03290i	−0.288207	−	0.251799i	−1.79078	−	3.71860i	0.413407	−	9.20523i	−2.79015	−	1.04716i	−3.18788	−	5.17550i
4.2	−2.28087	−	1.36276i	−0.217703	−	0.0395073i	2.39754	+	4.45537i	−2.21603	−	0.298704i	0.442714	+	0.386788i	1.95832	+	4.06648i	0.364706	−	8.12082i	−2.76287	−	1.03692i	4.64742	+	3.70122i
4.3	−2.24894	−	1.34368i	−1.38786	−	0.251859i	2.30452	+	4.28251i	1.12834	−	1.93050i	2.78279	+	2.43125i	0.508509	+	1.05593i	0.336527	−	7.49336i	−0.945985	−	0.355034i	−5.13155	+	2.82545i
4.4	−2.21712	−	1.32467i	2.16210	+	0.392364i	2.21314	+	4.11270i	−0.398218	−	2.20032i	−4.27389	−	3.73399i	0.223641	+	0.464395i	0.309422	−	6.88982i	1.71203	+	0.642537i	−2.03180	+	5.40589i
4.5	−2.20332	−	1.31642i	−1.84341	−	0.334530i	2.17391	+	4.03980i	−1.41303	+	1.73302i	3.62124	+	3.16378i	−0.499893	−	1.03804i	0.297963	−	6.63465i	0.477548	+	0.179227i	5.39473	−	1.95825i
4.6	−2.18130	−	1.30327i	3.21140	+	0.582784i	2.11184	+	3.92445i	1.33443	+	1.79424i	−6.24552	−	5.45655i	0.370306	+	0.768948i	0.280052	−	6.23585i	7.16478	+	2.68899i	−0.572413	−	5.65290i
4.7	−2.15375	−	1.28681i	−3.21146	−	0.582795i	2.03504	+	3.78174i	1.48142	+	1.67493i	6.16676	+	5.38773i	0.615446	+	1.27799i	0.258274	−	5.75091i	7.16515	+	2.68913i	−1.03531	−	5.51369i
4.8	−2.13969	−	1.27840i	1.81442	+	0.329269i	1.99620	+	3.70957i	−2.20970	+	0.342364i	−3.46136	−	3.02410i	−1.46091	−	3.03361i	0.247422	−	5.50928i	0.375013	+	0.140745i	5.16575	+	2.09234i
4.9	−1.96800	−	1.17582i	1.24922	+	0.226699i	1.54272	+	2.86685i	2.17891	−	0.502357i	−2.19190	−	1.91500i	0.936272	+	1.94419i	0.129140	−	2.87551i	−1.29955	−	0.487731i	−4.87877	−	1.57337i
4.10	−1.82363	−	1.08957i	0.956181	+	0.173521i	1.19073	+	2.21274i	0.0851828	+	2.23444i	−1.55466	−	1.35826i	1.73684	+	3.60658i	0.0488718	−	1.08822i	−1.92453	−	0.722289i	2.27924	−	4.16761i
4.11	−1.70207	−	1.01694i	−1.51388	−	0.274729i	0.915131	+	1.70060i	1.75880	+	1.38080i	2.29734	+	2.00713i	0.389167	+	0.808114i	−0.00612086	+	0.136292i	−0.592351	−	0.222313i	−1.58940	−	4.13881i
4.12	−1.70082	−	1.01619i	−3.19702	−	0.580174i	0.912409	+	1.69554i	−1.21455	−	1.87746i	4.84800	+	4.23557i	1.89196	+	3.92869i	−0.00662701	+	0.147562i	7.07566	+	2.65554i	0.157873	+	4.42745i
4.13	−1.67423	−	1.00030i	−1.28864	−	0.233854i	0.854692	+	1.58828i	1.09717	−	1.94839i	1.92355	+	1.68056i	0.129138	+	0.268157i	−0.0171808	+	0.382559i	−1.20280	−	0.451419i	−3.78589	+	2.16454i
4.14	−1.65958	−	0.991555i	−1.71659	−	0.311515i	0.823299	+	1.52995i	−1.86204	−	1.23807i	2.53993	+	2.21907i	−0.189409	−	0.393312i	−0.0227765	+	0.507159i	0.0409235	+	0.0153588i	1.86259	+	3.90099i
4.15	−1.61949	−	0.967599i	−0.107852	−	0.0195723i	0.738757	+	1.37284i	−0.356062	+	2.20754i	0.155727	+	0.136055i	−0.827813	−	1.71897i	−0.0373264	+	0.831138i	−2.79746	−	1.04990i	2.71265	−	3.23056i
4.16	−1.61165	−	0.962918i	−0.0816339	−	0.0148144i	0.722480	+	1.34259i	−1.82534	−	1.29156i	0.117301	+	0.102482i	−1.08204	−	2.24688i	−0.0400392	+	0.891542i	−2.80226	−	1.05171i	1.69816	+	3.83920i
4.17	−1.60269	−	0.957560i	−2.75047	−	0.499136i	0.703941	+	1.30814i	1.96928	−	1.05921i	3.93018	+	3.43369i	−2.16712	−	4.50007i	−0.0430932	+	0.959544i	4.50722	+	1.69159i	−4.17040	−	0.188130i
4.18	−1.56877	−	0.937299i	2.82082	+	0.511904i	0.634787	+	1.17963i	1.28947	−	1.82682i	−3.94543	−	3.44702i	−1.39105	−	2.88854i	−0.0541463	+	1.20566i	4.88628	+	1.83385i	−3.73516	+	1.65725i
4.19	−1.31977	−	0.788525i	1.92901	+	0.350064i	0.172280	+	0.320150i	−1.98290	+	1.03350i	−2.26981	−	1.98308i	0.115631	+	0.240109i	−0.112873	+	2.51331i	0.789833	+	0.296429i	3.43190	+	0.199590i
4.20	−1.30926	−	0.782244i	2.06659	+	0.375031i	0.154508	+	0.287124i	−0.872774	−	2.05870i	−2.41233	−	2.10759i	1.84445	+	3.83004i	−0.114540	+	2.55043i	1.32145	+	0.495948i	−0.467725	+	3.37809i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
25.e	even	10	1	inner
29.e	even	14	1	inner
725.bh	even	70	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	725.2.bh.a	✓	1728
25.e	even	10	1	inner	725.2.bh.a	✓	1728
29.e	even	14	1	inner	725.2.bh.a	✓	1728
725.bh	even	70	1	inner	725.2.bh.a	✓	1728

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
725.2.bh.a	✓	1728	1.a	even	1	1	trivial
725.2.bh.a	✓	1728	25.e	even	10	1	inner
725.2.bh.a	✓	1728	29.e	even	14	1	inner
725.2.bh.a	✓	1728	725.bh	even	70	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(725, [\chi])\).