Newform orbit 825.2.bv.a

• Label: 825.2.bv.a
• Level: $825$
• Weight: $2$
• Character orbit: 825.bv
• Analytic conductor: $6.588$
• Analytic rank: $0$
• Dimension: $240$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.bv (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.58765816676\)
Analytic rank:	\(0\)
Dimension:	\(240\)
Relative dimension:	\(60\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 240 q + 60 q^{4} + 6 q^{5} + 4 q^{6} + 20 q^{7} - 240 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
229.1	−1.62533	+	2.23707i			1.00000i	−1.74477	−	5.36984i	−0.865518	−	2.06177i	−2.23707	−	1.62533i	1.90098	−	2.61647i	9.58887	+	3.11561i	−1.00000			6.01907	+	1.41482i
229.2	−1.59021	+	2.18873i		−	1.00000i	−1.64375	−	5.05895i	2.23177	+	0.138541i	2.18873	+	1.59021i	2.63011	−	3.62003i	8.54058	+	2.77500i	−1.00000			−3.85221	+	4.66444i
229.3	−1.51767	+	2.08889i			1.00000i	−1.44212	−	4.43840i	1.21469	+	1.87737i	−2.08889	−	1.51767i	1.01347	−	1.39492i	6.54873	+	2.12781i	−1.00000			−5.76513	−	0.311869i
229.4	−1.50176	+	2.06699i		−	1.00000i	−1.39915	−	4.30613i	0.108640	+	2.23343i	2.06699	+	1.50176i	−2.78784	+	3.83714i	6.14213	+	1.99570i	−1.00000			−4.77963	−	3.12951i
229.5	−1.45343	+	2.00048i			1.00000i	−1.27141	−	3.91300i	1.75158	−	1.38995i	−2.00048	−	1.45343i	−1.92985	+	2.65621i	4.97238	+	1.61562i	−1.00000			0.234761	+	5.52420i
229.6	−1.44907	+	1.99448i		−	1.00000i	−1.26009	−	3.87817i	0.402508	−	2.19954i	1.99448	+	1.44907i	−1.80478	+	2.48406i	4.87158	+	1.58287i	−1.00000			3.80367	+	3.99009i
229.7	−1.44038	+	1.98251i		−	1.00000i	−1.23762	−	3.80901i	−2.19799	−	0.410908i	1.98251	+	1.44038i	−0.163390	+	0.224887i	4.67288	+	1.51831i	−1.00000			3.98056	−	3.76567i
229.8	−1.32445	+	1.82295i		−	1.00000i	−0.950938	−	2.92669i	0.452325	−	2.18984i	1.82295	+	1.32445i	0.988725	−	1.36086i	2.30866	+	0.750129i	−1.00000			3.39288	+	3.72490i
229.9	−1.29970	+	1.78888i			1.00000i	−0.892845	−	2.74790i	−0.423658	+	2.19557i	−1.78888	−	1.29970i	1.35421	−	1.86391i	1.87018	+	0.607657i	−1.00000			−3.37698	−	3.61145i
229.10	−1.28616	+	1.77025i			1.00000i	−0.861544	−	2.65156i	−1.34605	−	1.78554i	−1.77025	−	1.28616i	−0.879948	+	1.21114i	1.63990	+	0.532837i	−1.00000			4.89210	−	0.0863584i
229.11	−1.12467	+	1.54798i			1.00000i	−0.513321	−	1.57984i	1.17143	+	1.90466i	−1.54798	−	1.12467i	−2.69745	+	3.71273i	−0.616642	−	0.200359i	−1.00000			−4.26587	−	0.328774i
229.12	−1.10426	+	1.51988i		−	1.00000i	−0.472624	−	1.45459i	1.94145	+	1.10941i	1.51988	+	1.10426i	0.876577	−	1.20651i	−0.840761	−	0.273180i	−1.00000			−3.83004	+	1.72570i
229.13	−1.09709	+	1.51001i		−	1.00000i	−0.458504	−	1.41113i	−1.21793	+	1.87527i	1.51001	+	1.09709i	1.35490	−	1.86487i	−0.916408	−	0.297759i	−1.00000			−1.49551	−	3.89643i
229.14	−0.971558	+	1.33724i			1.00000i	−0.226238	−	0.696290i	−2.09029	−	0.794156i	−1.33724	−	0.971558i	0.542949	−	0.747306i	−1.99312	−	0.647604i	−1.00000			3.09281	−	2.02364i
229.15	−0.907749	+	1.24941i			1.00000i	−0.118981	−	0.366186i	2.17166	−	0.532824i	−1.24941	−	0.907749i	2.88816	−	3.97521i	−2.37202	−	0.770715i	−1.00000			−1.30560	+	3.19696i
229.16	−0.889988	+	1.22496i			1.00000i	−0.0904232	−	0.278294i	−1.65681	+	1.50166i	−1.22496	−	0.889988i	0.788000	−	1.08459i	−2.45869	−	0.798876i	−1.00000			−0.364931	−	3.36599i
229.17	−0.747547	+	1.02891i		−	1.00000i	0.118205	+	0.363797i	−1.85789	+	1.24428i	1.02891	+	0.747547i	−1.11081	+	1.52890i	−2.88179	−	0.936350i	−1.00000			0.108603	−	2.84176i
229.18	−0.727132	+	1.00081i		−	1.00000i	0.145131	+	0.446668i	−2.05997	−	0.869789i	1.00081	+	0.727132i	−2.52673	+	3.47774i	−2.90561	−	0.944090i	−1.00000			2.36836	−	1.42919i
229.19	−0.703708	+	0.968572i			1.00000i	0.175109	+	0.538929i	0.963916	−	2.01764i	−0.968572	−	0.703708i	−2.17421	+	2.99254i	−2.92247	−	0.949566i	−1.00000			1.27591	+	2.35345i
229.20	−0.702299	+	0.966631i		−	1.00000i	0.176882	+	0.544385i	−0.811320	−	2.08369i	0.966631	+	0.702299i	1.40869	−	1.93889i	−2.92313	−	0.949782i	−1.00000			2.58395	+	0.679125i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
275.t	even	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	825.2.bv.a	yes	240
11.c	even	5	1		825.2.v.a	✓	240
25.e	even	10	1		825.2.v.a	✓	240
275.t	even	10	1	inner	825.2.bv.a	yes	240

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
825.2.v.a	✓	240	11.c	even	5	1
825.2.v.a	✓	240	25.e	even	10	1
825.2.bv.a	yes	240	1.a	even	1	1	trivial
825.2.bv.a	yes	240	275.t	even	10	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(825, [\chi])\).