Newform orbit 145.2.e.a

• Label: 145.2.e.a
• Level: $145$
• Weight: $2$
• Character orbit: 145.e
• Analytic conductor: $1.158$
• Analytic rank: $0$
• Dimension: $26$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	145.e (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.15783082931\)
Analytic rank:	\(0\)
Dimension:	\(26\)
Relative dimension:	\(13\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 26 q - 4 q^{3} - 22 q^{4} - 4 q^{7} + 10 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
12.1		−	2.73482i	1.63186			−5.47925			0.903087	−	2.04559i		−	4.46285i	1.05887	+	1.05887i			9.51511i	−0.337028			−5.59432	−	2.46978i
12.2		−	2.41122i	−1.85973			−3.81399			−1.59267	+	1.56952i			4.48422i	−0.291676	−	0.291676i			4.37394i	0.458586			3.78447	+	3.84028i
12.3		−	1.82099i	2.59340			−1.31599			−1.75450	+	1.38626i		−	4.72256i	−0.820621	−	0.820621i		−	1.24557i	3.72575			2.52437	+	3.19492i
12.4		−	1.77873i	−1.38965			−1.16389			2.14366	−	0.636182i			2.47181i	−3.41296	−	3.41296i		−	1.48721i	−1.06888			−1.13160	−	3.81300i
12.5		−	1.36192i	−0.228160			0.145179			1.87852	+	1.21291i			0.310736i	3.45046	+	3.45046i		−	2.92156i	−2.94794			1.65188	−	2.55840i
12.6		−	0.839004i	0.711801			1.29607			−1.24503	−	1.85739i		−	0.597203i	1.13987	+	1.13987i		−	2.76542i	−2.49334			−1.55836	+	1.04459i
12.7		−	0.342532i	−2.64611			1.88267			−1.82632	−	1.29018i			0.906377i	−1.55474	−	1.55474i		−	1.32994i	4.00189			−0.441927	+	0.625573i
12.8			0.222351i	1.02589			1.95056			0.621451	+	2.14798i			0.228107i	−2.35964	−	2.35964i			0.878412i	−1.94756			−0.477605	+	0.138180i
12.9			0.895351i	−2.11245			1.19835			1.71183	−	1.43862i		−	1.89138i	1.38465	+	1.38465i			2.86364i	1.46244			1.28807	+	1.53269i
12.10			1.26373i	−0.913274			0.402981			−1.78577	+	1.34575i		−	1.15413i	2.03055	+	2.03055i			3.03672i	−2.16593			−1.70067	−	2.25673i
12.11			1.41066i	2.58872			0.0100302			−1.93694	−	1.11726i			3.65181i	−0.510628	−	0.510628i			2.83547i	3.70148			1.57607	−	2.73237i
12.12			2.23019i	1.25170			−2.97373			2.19887	−	0.406147i			2.79153i	0.483409	+	0.483409i		−	2.17160i	−1.43324			0.905783	+	4.90390i
12.13			2.26693i	−2.65401			−3.13899			0.683805	+	2.12895i		−	6.01647i	−2.59753	−	2.59753i		−	2.58201i	4.04378			−4.82618	+	1.55014i
133.1		−	2.26693i	−2.65401			−3.13899			0.683805	−	2.12895i			6.01647i	−2.59753	+	2.59753i			2.58201i	4.04378			−4.82618	−	1.55014i
133.2		−	2.23019i	1.25170			−2.97373			2.19887	+	0.406147i		−	2.79153i	0.483409	−	0.483409i			2.17160i	−1.43324			0.905783	−	4.90390i
133.3		−	1.41066i	2.58872			0.0100302			−1.93694	+	1.11726i		−	3.65181i	−0.510628	+	0.510628i		−	2.83547i	3.70148			1.57607	+	2.73237i
133.4		−	1.26373i	−0.913274			0.402981			−1.78577	−	1.34575i			1.15413i	2.03055	−	2.03055i		−	3.03672i	−2.16593			−1.70067	+	2.25673i
133.5		−	0.895351i	−2.11245			1.19835			1.71183	+	1.43862i			1.89138i	1.38465	−	1.38465i		−	2.86364i	1.46244			1.28807	−	1.53269i
133.6		−	0.222351i	1.02589			1.95056			0.621451	−	2.14798i		−	0.228107i	−2.35964	+	2.35964i		−	0.878412i	−1.94756			−0.477605	−	0.138180i
133.7			0.342532i	−2.64611			1.88267			−1.82632	+	1.29018i		−	0.906377i	−1.55474	+	1.55474i			1.32994i	4.00189			−0.441927	−	0.625573i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
145.e	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	145.2.e.a	✓	26
5.b	even	2	1		725.2.e.c		26
5.c	odd	4	1		145.2.j.a	yes	26
5.c	odd	4	1		725.2.j.c		26
29.c	odd	4	1		145.2.j.a	yes	26
145.e	even	4	1	inner	145.2.e.a	✓	26
145.f	odd	4	1		725.2.j.c		26
145.j	even	4	1		725.2.e.c		26

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
145.2.e.a	✓	26	1.a	even	1	1	trivial
145.2.e.a	✓	26	145.e	even	4	1	inner
145.2.j.a	yes	26	5.c	odd	4	1
145.2.j.a	yes	26	29.c	odd	4	1
725.2.e.c		26	5.b	even	2	1
725.2.e.c		26	145.j	even	4	1
725.2.j.c		26	5.c	odd	4	1
725.2.j.c		26	145.f	odd	4	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(145, [\chi])\).