Newform orbit 950.2.w.a

• Label: 950.2.w.a
• Level: $950$
• Weight: $2$
• Character orbit: 950.w
• Analytic conductor: $7.586$
• Analytic rank: $0$
• Dimension: $400$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.w (of order \(20\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.58578819202\)
Analytic rank:	\(0\)
Dimension:	\(400\)
Relative dimension:	\(50\) over \(\Q(\zeta_{20})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 400q + 4q^{5} - 4q^{7} + O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
37.1	−0.987688	+	0.156434i	−1.41733	+	2.78167i	0.951057	−	0.309017i	2.23282	−	0.120389i	0.964734	−	2.96915i	3.07932	+	3.07932i	−0.891007	+	0.453990i	−3.96551	−	5.45806i	−2.18650	+	0.468198i
37.2	−0.987688	+	0.156434i	−1.40212	+	2.75181i	0.951057	−	0.309017i	−1.82971	−	1.28537i	0.954377	−	2.93727i	−1.62377	−	1.62377i	−0.891007	+	0.453990i	−3.84317	−	5.28967i	2.00826	+	0.983314i
37.3	−0.987688	+	0.156434i	−1.32806	+	2.60647i	0.951057	−	0.309017i	1.06510	+	1.96610i	0.903971	−	2.78214i	−0.494215	−	0.494215i	−0.891007	+	0.453990i	−3.26659	−	4.49607i	−1.35955	−	1.77528i
37.4	−0.987688	+	0.156434i	−1.26480	+	2.48231i	0.951057	−	0.309017i	−1.52838	+	1.63219i	0.860911	−	2.64961i	−1.59067	−	1.59067i	−0.891007	+	0.453990i	−2.79880	−	3.85222i	1.25423	−	1.85119i
37.5	−0.987688	+	0.156434i	−1.00551	+	1.97343i	0.951057	−	0.309017i	1.74220	−	1.40169i	0.684420	−	2.10643i	−1.24411	−	1.24411i	−0.891007	+	0.453990i	−1.12001	−	1.54156i	−1.50148	+	1.65697i
37.6	−0.987688	+	0.156434i	−0.966228	+	1.89633i	0.951057	−	0.309017i	−0.861084	−	2.06362i	0.657681	−	2.02413i	2.78834	+	2.78834i	−0.891007	+	0.453990i	−0.899114	−	1.23752i	1.17330	+	1.90351i
37.7	−0.987688	+	0.156434i	−0.669280	+	1.31354i	0.951057	−	0.309017i	−2.09747	+	0.775001i	0.455558	−	1.40206i	1.60624	+	1.60624i	−0.891007	+	0.453990i	0.485913	+	0.668802i	1.95041	−	1.09358i
37.8	−0.987688	+	0.156434i	−0.581458	+	1.14117i	0.951057	−	0.309017i	1.37992	+	1.75950i	0.395780	−	1.21809i	1.14962	+	1.14962i	−0.891007	+	0.453990i	0.799169	+	1.09996i	−1.63817	−	1.52197i
37.9	−0.987688	+	0.156434i	−0.380740	+	0.747244i	0.951057	−	0.309017i	2.16957	+	0.541276i	0.259158	−	0.797606i	−1.83916	−	1.83916i	−0.891007	+	0.453990i	1.34994	+	1.85804i	−2.22753	−	0.195217i
37.10	−0.987688	+	0.156434i	−0.341841	+	0.670901i	0.951057	−	0.309017i	0.0404826	−	2.23570i	0.232680	−	0.716117i	2.21716	+	2.21716i	−0.891007	+	0.453990i	1.43010	+	1.96837i	0.309757	+	2.21451i
37.11	−0.987688	+	0.156434i	−0.172149	+	0.337861i	0.951057	−	0.309017i	−1.08112	+	1.95734i	0.117176	−	0.360631i	−2.52947	−	2.52947i	−0.891007	+	0.453990i	1.67884	+	2.31073i	0.761613	−	2.10237i
37.12	−0.987688	+	0.156434i	−0.140807	+	0.276349i	0.951057	−	0.309017i	0.842195	+	2.07140i	0.0958429	−	0.294974i	2.00698	+	2.00698i	−0.891007	+	0.453990i	1.70681	+	2.34923i	−1.15586	−	1.91415i
37.13	−0.987688	+	0.156434i	−0.0204485	+	0.0401324i	0.951057	−	0.309017i	−2.01849	−	0.962141i	0.0139186	−	0.0428372i	−1.29403	−	1.29403i	−0.891007	+	0.453990i	1.76216	+	2.42541i	2.14415	+	0.634534i
37.14	−0.987688	+	0.156434i	0.0539197	−	0.105823i	0.951057	−	0.309017i	0.164450	−	2.23001i	−0.0367014	+	0.112955i	−3.59050	−	3.59050i	−0.891007	+	0.453990i	1.75506	+	2.41564i	0.186426	+	2.22828i
37.15	−0.987688	+	0.156434i	0.146430	−	0.287385i	0.951057	−	0.309017i	2.22675	−	0.203946i	−0.0996703	+	0.306754i	−0.119348	−	0.119348i	−0.891007	+	0.453990i	1.70221	+	2.34289i	−2.16743	+	0.549775i
37.16	−0.987688	+	0.156434i	0.299107	−	0.587030i	0.951057	−	0.309017i	−2.03682	−	0.922698i	−0.203592	+	0.626593i	−0.375210	−	0.375210i	−0.891007	+	0.453990i	1.50822	+	2.07588i	2.15608	+	0.592709i
37.17	−0.987688	+	0.156434i	0.531107	−	1.04236i	0.951057	−	0.309017i	−1.52005	+	1.63996i	−0.361507	+	1.11261i	3.11636	+	3.11636i	−0.891007	+	0.453990i	0.958925	+	1.31985i	1.24479	−	1.85755i
37.18	−0.987688	+	0.156434i	0.672164	−	1.31920i	0.951057	−	0.309017i	0.922100	−	2.03709i	−0.457521	+	1.40810i	1.03073	+	1.03073i	−0.891007	+	0.453990i	0.474883	+	0.653621i	−0.592076	+	2.15626i
37.19	−0.987688	+	0.156434i	0.888230	−	1.74325i	0.951057	−	0.309017i	−1.88136	+	1.20850i	−0.604590	+	1.86074i	−1.93054	−	1.93054i	−0.891007	+	0.453990i	−0.486612	−	0.669764i	1.66915	−	1.48793i
37.20	−0.987688	+	0.156434i	0.966230	−	1.89633i	0.951057	−	0.309017i	0.684737	+	2.12865i	−0.657682	+	2.02414i	0.498269	+	0.498269i	−0.891007	+	0.453990i	−0.899122	−	1.23753i	−1.00930	−	1.99532i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
19.b	odd	2	1	inner
25.f	odd	20	1	inner
475.v	even	20	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	950.2.w.a	✓	400
19.b	odd	2	1	inner	950.2.w.a	✓	400
25.f	odd	20	1	inner	950.2.w.a	✓	400
475.v	even	20	1	inner	950.2.w.a	✓	400

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
950.2.w.a	✓	400	1.a	even	1	1	trivial
950.2.w.a	✓	400	19.b	odd	2	1	inner
950.2.w.a	✓	400	25.f	odd	20	1	inner
950.2.w.a	✓	400	475.v	even	20	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(950, [\chi])\).