Newform orbit 567.2.bd.a

• Label: 567.2.bd.a
• Level: $567$
• Weight: $2$
• Character orbit: 567.bd
• Analytic conductor: $4.528$
• Analytic rank: $0$
• Dimension: $132$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.bd (of order \(18\), degree \(6\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.52751779461\)
Analytic rank:	\(0\)
Dimension:	\(132\)
Relative dimension:	\(22\) over \(\Q(\zeta_{18})\)
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 - 9 * q^10 - 9 * q^11 + 42 * q^14 - 15 * q^16 + 9 * q^17 - 9 * q^19 + 18 * q^20 - 12 * q^22 - 30 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 + 51 * q^32 + 18 * q^34 + 9 * q^35 - 6 * q^37 + 9 * q^38 - 9 * q^40 - 12 * q^43 - 6 * q^46 - 45 * q^47 + 30 * q^49 + 9 * q^50 - 9 * q^52 - 45 * q^53 + 51 * q^56 - 3 * q^58 + 9 * q^59 - 63 * q^61 - 99 * q^62 + 18 * q^64 + 102 * q^65 - 3 * q^67 - 144 * q^68 - 15 * q^70 - 18 * q^71 + 33 * q^74 - 36 * q^76 + 57 * q^77 - 21 * q^79 + 72 * q^80 - 18 * q^82 - 90 * q^83 + 9 * q^85 + 33 * q^86 + 45 * q^88 + 9 * q^89 - 21 * q^91 - 150 * q^92 - 9 * q^94 - 27 * q^95 + 180 * 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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
17.1	−2.50283	+	0.441316i		0		4.19001	−	1.52504i	0.437341	−	0.159179i		0		−1.48170	+	2.19193i	−5.41196	+	3.12460i		0		−1.02434	+	0.591403i
17.2	−2.45739	+	0.433304i		0		3.97163	−	1.44555i	0.335948	−	0.122275i		0		0.0666399	−	2.64491i	−4.81149	+	2.77792i		0		−0.772573	+	0.446045i
17.3	−2.22112	+	0.391643i		0		2.90060	−	1.05573i	3.20807	−	1.16764i		0		−2.62457	−	0.334082i	−2.12267	+	1.22552i		0		−6.66821	+	3.84989i
17.4	−1.87320	+	0.330296i		0		1.52040	−	0.553380i	0.848304	−	0.308757i		0		2.48993	+	0.894564i	0.629295	−	0.363324i		0		−1.48706	+	0.858555i
17.5	−1.66985	+	0.294440i		0		0.822331	−	0.299304i	−1.39543	+	0.507895i		0		−0.356869	−	2.62157i	1.65184	−	0.953692i		0		2.18062	−	1.25898i
17.6	−1.65422	+	0.291684i		0		0.771989	−	0.280981i	−3.52188	+	1.28186i		0		−2.17331	+	1.50888i	1.71431	−	0.989760i		0		5.45209	−	3.14776i
17.7	−1.10401	+	0.194666i		0		−0.698446	+	0.254214i	3.85196	−	1.40200i		0		2.61259	−	0.417595i	2.66330	−	1.53766i		0		−3.97967	+	2.29767i
17.8	−0.892534	+	0.157378i		0		−1.10754	+	0.403110i	1.14226	−	0.415747i		0		−1.98483	+	1.74942i	2.49483	−	1.44039i		0		−0.954073	+	0.550834i
17.9	−0.882178	+	0.155552i		0		−1.12534	+	0.409592i	−0.123522	+	0.0449584i		0		1.69913	+	2.02805i	2.48059	−	1.43217i		0		0.101975	−	0.0588754i
17.10	−0.245063	+	0.0432112i		0		−1.82120	+	0.662861i	−1.99870	+	0.727467i		0		0.302346	−	2.62842i	0.848674	−	0.489982i		0		0.458373	−	0.264642i
17.11	−0.0159182	+	0.00280680i		0		−1.87914	+	0.683951i	−3.75147	+	1.36542i		0		0.157938	+	2.64103i	0.0559891	−	0.0323253i		0		0.0558840	−	0.0322646i
17.12	0.0147002	−	0.00259205i		0		−1.87918	+	0.683964i	−1.54651	+	0.562885i		0		2.21011	−	1.45445i	−0.0517058	+	0.0298524i		0		−0.0212751	+	0.0122832i
17.13	0.313923	−	0.0553531i		0		−1.78390	+	0.649287i	2.68563	−	0.977491i		0		−2.48320	−	0.913082i	−1.07619	+	0.621337i		0		0.788975	−	0.455515i
17.14	0.877614	−	0.154747i		0		−1.13313	+	0.412424i	1.30288	−	0.474210i		0		1.81190	+	1.92796i	−2.47415	+	1.42845i		0		1.07004	−	0.617790i
17.15	0.910598	−	0.160563i		0		−1.07598	+	0.391623i	0.473927	−	0.172495i		0		−2.46079	−	0.971863i	−2.51844	+	1.45402i		0		0.403861	−	0.233169i
17.16	1.38665	−	0.244504i		0		−0.0163608	+	0.00595485i	−1.98299	+	0.721749i		0		−2.18605	−	1.49037i	−2.46004	+	1.42030i		0		−2.57325	+	1.48566i
17.17	1.57155	−	0.277106i		0		0.513586	−	0.186930i	−1.78318	+	0.649025i		0		−1.28547	+	2.31248i	−2.00866	+	1.15970i		0		−2.62250	+	1.51410i
17.18	1.63190	−	0.287749i		0		0.700923	−	0.255115i	3.60525	−	1.31220i		0		2.03118	−	1.69538i	−1.79971	+	1.03907i		0		5.50583	−	3.17879i
17.19	2.06025	−	0.363278i		0		2.23328	−	0.812849i	−0.338534	+	0.123216i		0		1.84499	−	1.89632i	0.682329	−	0.393943i		0		−0.652704	+	0.376839i
17.20	2.26715	−	0.399760i		0		3.10078	−	1.12859i	1.73217	−	0.630457i		0		0.678971	+	2.55715i	2.59137	−	1.49613i		0		3.67505	−	2.12179i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
189.bd	even	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	567.2.bd.a		132
3.b	odd	2	1		189.2.bd.a	yes	132
7.d	odd	6	1		567.2.ba.a		132
21.g	even	6	1		189.2.ba.a	✓	132
27.e	even	9	1		189.2.ba.a	✓	132
27.f	odd	18	1		567.2.ba.a		132
189.z	odd	18	1		189.2.bd.a	yes	132
189.bd	even	18	1	inner	567.2.bd.a		132

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
189.2.ba.a	✓	132	21.g	even	6	1
189.2.ba.a	✓	132	27.e	even	9	1
189.2.bd.a	yes	132	3.b	odd	2	1
189.2.bd.a	yes	132	189.z	odd	18	1
567.2.ba.a		132	7.d	odd	6	1
567.2.ba.a		132	27.f	odd	18	1
567.2.bd.a		132	1.a	even	1	1	trivial
567.2.bd.a		132	189.bd	even	18	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(567, [\chi])\).