Newform orbit 1915.2.c.a

• Label: 1915.2.c.a
• Level: $1915$
• Weight: $2$
• Character orbit: 1915.c
• Analytic conductor: $15.291$
• Analytic rank: $0$
• Dimension: $190$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1915 = 5 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1915.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(15.2913519871\)
Analytic rank:	\(0\)
Dimension:	\(190\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 190 q - 188 q^{4} - 4 q^{6} - 186 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
384.1		−	2.82450i			2.32912i	−5.97781			−2.19713	+	0.415456i	6.57859				−	0.620081i			11.2353i	−2.42478			1.17345	+	6.20581i
384.2		−	2.77261i		−	0.285202i	−5.68734			0.700664	+	2.12346i	−0.790752				−	2.79046i			10.2235i	2.91866			5.88751	−	1.94267i
384.3		−	2.74379i		−	1.99643i	−5.52838			−1.95117	−	1.09222i	−5.47779					3.53282i			9.68112i	−0.985748			−2.99682	+	5.35359i
384.4		−	2.73730i		−	2.14029i	−5.49280			−0.301895	+	2.21559i	−5.85861					0.398139i			9.56085i	−1.58083			6.06474	+	0.826376i
384.5		−	2.68469i			0.951315i	−5.20755			1.01533	−	1.99226i	2.55398					3.51008i			8.61126i	2.09500			−5.34860	−	2.72585i
384.6		−	2.67520i		−	2.42046i	−5.15668			0.149901	−	2.23104i	−6.47521				−	5.18983i			8.44475i	−2.85862			−5.96847	−	0.401016i
384.7		−	2.66724i		−	3.24732i	−5.11417			2.21593	−	0.299395i	−8.66138					3.41644i			8.30623i	−7.54507			−0.798559	−	5.91043i
384.8		−	2.64663i		−	1.59060i	−5.00465			2.23605	−	0.00801240i	−4.20972				−	1.34010i			7.95218i	0.470005			−0.0212059	−	5.91800i
384.9		−	2.62898i			0.577029i	−4.91152			2.16906	−	0.543305i	1.51700					0.118762i			7.65430i	2.66704			−1.42833	−	5.70241i
384.10		−	2.61783i			1.28257i	−4.85306			1.31428	+	1.80905i	3.35755					4.95392i			7.46884i	1.35502			4.73579	−	3.44058i
384.11		−	2.57726i			0.137809i	−4.64225			−1.22409	−	1.87126i	0.355168				−	1.54749i			6.80976i	2.98101			−4.82272	+	3.15478i
384.12		−	2.55995i			2.42392i	−4.55335			−0.131293	−	2.23221i	6.20513				−	3.31404i			6.53646i	−2.87540			−5.71435	+	0.336105i
384.13		−	2.53476i			3.22937i	−4.42500			1.91436	−	1.15553i	8.18566					0.912560i			6.14678i	−7.42882			−2.92898	−	4.85243i
384.14		−	2.50844i			0.415497i	−4.29227			−1.32095	+	1.80419i	1.04225				−	1.70376i			5.75002i	2.82736			4.52570	+	3.31352i
384.15		−	2.45004i			1.35099i	−4.00268			2.17959	+	0.499405i	3.30997				−	3.30935i			4.90663i	1.17483			1.22356	−	5.34006i
384.16		−	2.44055i			2.71788i	−3.95631			0.617234	+	2.14919i	6.63312				−	3.22836i			4.77447i	−4.38685			5.24522	−	1.50639i
384.17		−	2.37402i		−	0.686699i	−3.63596			−2.06924	−	0.847493i	−1.63024					1.25097i			3.88379i	2.52844			−2.01196	+	4.91241i
384.18		−	2.37010i		−	0.562159i	−3.61736			−2.14898	+	0.617972i	−1.33237				−	5.06755i			3.83330i	2.68398			1.46465	+	5.09329i
384.19		−	2.33648i		−	2.56267i	−3.45915			−1.91927	+	1.14735i	−5.98764				−	2.01013i			3.40928i	−3.56730			2.68077	+	4.48433i
384.20		−	2.32890i			3.08132i	−3.42377			−0.849883	+	2.06826i	7.17608					3.03297i			3.31583i	−6.49452			4.81677	+	1.97929i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1915.2.c.a	✓	190
5.b	even	2	1	inner	1915.2.c.a	✓	190
5.c	odd	4	1		9575.2.a.m		95
5.c	odd	4	1		9575.2.a.n		95

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1915.2.c.a	✓	190	1.a	even	1	1	trivial
1915.2.c.a	✓	190	5.b	even	2	1	inner
9575.2.a.m		95	5.c	odd	4	1
9575.2.a.n		95	5.c	odd	4	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(1915, [\chi])\).