Newform orbit 900.2.v.b

• Label: 900.2.v.b
• Level: $900$
• Weight: $2$
• Character orbit: 900.v
• Analytic conductor: $7.187$
• Analytic rank: $0$
• Dimension: $224$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.v (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.18653618192\)
Analytic rank:	\(0\)
Dimension:	\(224\)
Relative dimension:	\(56\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 224 q - 8 q^{4}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
71.1	−1.40993	−	0.110020i		0		1.97579	+	0.310239i	−1.15492	+	1.91472i		0				4.16958i	−2.75159	−	0.654790i		0		1.83901	−	2.57255i
71.2	−1.40774	+	0.135159i		0		1.96346	−	0.380537i	2.23373	+	0.102263i		0			−	1.26741i	−2.71261	+	0.801076i		0		−3.15833	+	0.157948i
71.3	−1.40145	+	0.189576i		0		1.92812	−	0.531361i	2.20930	−	0.344985i		0				3.61007i	−2.60143	+	1.11020i		0		−3.03082	+	0.902307i
71.4	−1.36015	−	0.387300i		0		1.70000	+	1.05357i	−0.338756	−	2.21026i		0				3.76831i	−1.90420	−	2.09142i		0		−0.395276	+	3.13748i
71.5	−1.35751	+	0.396441i		0		1.68567	−	1.07635i	−1.11652	−	1.93736i		0			−	4.01981i	−1.86161	+	2.12942i		0		2.28374	+	2.18736i
71.6	−1.34433	+	0.439051i		0		1.61447	−	1.18046i	0.413768	+	2.19745i		0				0.500941i	−1.65210	+	2.29577i		0		−1.52104	−	2.77244i
71.7	−1.32803	−	0.486142i		0		1.52733	+	1.29122i	−0.338756	−	2.21026i		0			−	3.76831i	−1.40063	−	2.45728i		0		−0.624621	+	3.09998i
71.8	−1.28785	+	0.584328i		0		1.31712	−	1.50505i	−2.17612	−	0.514279i		0			−	0.743481i	−0.816813	+	2.70792i		0		3.10303	−	0.609255i
71.9	−1.20532	−	0.739727i		0		0.905608	+	1.78322i	−1.15492	+	1.91472i		0			−	4.16958i	0.227546	−	2.81926i		0		2.80843	−	1.45353i
71.10	−1.13088	+	0.849187i		0		0.557764	−	1.92065i	0.504670	+	2.17837i		0			−	1.75581i	1.00023	+	2.64567i		0		−2.42056	−	2.03491i
71.11	−1.05944	−	0.936795i		0		0.244832	+	1.98496i	2.23373	+	0.102263i		0				1.26741i	1.60011	−	2.33230i		0		−2.27070	−	2.20089i
71.12	−1.02237	−	0.977121i		0		0.0904680	+	1.99795i	2.20930	−	0.344985i		0			−	3.61007i	1.85975	−	2.13104i		0		−2.59580	−	1.80605i
71.13	−0.978165	+	1.02137i		0		−0.0863871	−	1.99813i	−1.52308	+	1.63714i		0			−	0.652662i	2.12533	+	1.86627i		0		−0.182298	−	3.15702i
71.14	−0.962619	+	1.03603i		0		−0.146730	−	1.99461i	1.64354	−	1.51617i		0				2.39469i	2.20773	+	1.76803i		0		−0.0112974	+	3.16226i
71.15	−0.915667	+	1.07775i		0		−0.323107	−	1.97373i	−1.28650	−	1.82891i		0				1.44868i	2.42305	+	1.45905i		0		3.14912	+	0.288136i
71.16	−0.886808	+	1.10162i		0		−0.427142	−	1.95385i	2.23533	+	0.0574551i		0				4.18415i	2.53120	+	1.26214i		0		−2.04560	+	2.41154i
71.17	−0.865227	−	1.11865i		0		−0.502766	+	1.93578i	−1.11652	−	1.93736i		0				4.01981i	2.60047	−	1.11246i		0		−1.20119	+	2.92526i
71.18	−0.829522	−	1.14538i		0		−0.623788	+	1.90023i	0.413768	+	2.19745i		0			−	0.500941i	2.69393	−	0.861811i		0		2.17369	−	2.29676i
71.19	−0.737145	+	1.20690i		0		−0.913234	−	1.77933i	0.880067	−	2.05560i		0			−	4.89989i	2.82066	+	0.209436i		0		1.83217	+	2.57743i
71.20	−0.698435	−	1.22971i		0		−1.02438	+	1.71775i	−2.17612	−	0.514279i		0				0.743481i	2.82779	+	0.0599570i		0		0.887466	+	3.03519i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
4.b	odd	2	1	inner
12.b	even	2	1	inner
25.d	even	5	1	inner
75.j	odd	10	1	inner
100.j	odd	10	1	inner
300.n	even	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	900.2.v.b	✓	224
3.b	odd	2	1	inner	900.2.v.b	✓	224
4.b	odd	2	1	inner	900.2.v.b	✓	224
12.b	even	2	1	inner	900.2.v.b	✓	224
25.d	even	5	1	inner	900.2.v.b	✓	224
75.j	odd	10	1	inner	900.2.v.b	✓	224
100.j	odd	10	1	inner	900.2.v.b	✓	224
300.n	even	10	1	inner	900.2.v.b	✓	224

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
900.2.v.b	✓	224	1.a	even	1	1	trivial
900.2.v.b	✓	224	3.b	odd	2	1	inner
900.2.v.b	✓	224	4.b	odd	2	1	inner
900.2.v.b	✓	224	12.b	even	2	1	inner
900.2.v.b	✓	224	25.d	even	5	1	inner
900.2.v.b	✓	224	75.j	odd	10	1	inner
900.2.v.b	✓	224	100.j	odd	10	1	inner
900.2.v.b	✓	224	300.n	even	10	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T7^56 + 238*T7^54 + 26443*T7^52 + 1823150*T7^50 + 87468285*T7^48 + 3103890308*T7^46 + 84545276574*T7^44 + 1810865085664*T7^42 + 31001111510040*T7^40 + 428937806995400*T7^38 + 4832617936470468*T7^36 + 44545619910612044*T7^34 + 336821589951355239*T7^32 + 2090949490259622810*T7^30 + 10650002234390796685*T7^28 + 44413742068675482830*T7^26 + 151123157108438552740*T7^24 + 417456936883495471590*T7^22 + 929846967519710394005*T7^20 + 1655154103964616095310*T7^18 + 2326960237664267609025*T7^16 + 2544182070732182388500*T7^14 + 2119261243647853887700*T7^12 + 1307954823990356676600*T7^10 + 575267865788172860200*T7^8 + 170311267551534522800*T7^6 + 30993069170036315200*T7^4 + 2930544664824398400*T7^2 + 94693488751112400