Newform orbit 7.19.d.a

• Label: 7.19.d.a
• Level: $7$
• Weight: $19$
• Character orbit: 7.d
• Analytic conductor: $14.377$
• Analytic rank: $0$
• Dimension: $22$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 19 \)
Character orbit:	\([\chi]\)	\(=\)	7.d (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.3770296397\)
Analytic rank:	\(0\)
Dimension:	\(22\)
Relative dimension:	\(11\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 22 q + 84 q^{2} - 3 q^{3} - 1395636 q^{4} - 2135115 q^{5} + 63763714 q^{7} + 97592448 q^{8} + 1382197506 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3.1	−466.935	−	808.755i	−25633.8	−	14799.7i	−304984.	+	528248.i	1.26391e6	−	729717.i			2.76419e7i	3.62612e7	−	1.77070e7i	3.24822e8			2.44350e8	+	4.23226e8i	−1.18032e9	−	6.81460e8i
3.2	−409.505	−	709.284i	18896.5	+	10909.9i	−204317.	+	353887.i	−2.42095e6	+	1.39774e6i		−	1.78707e7i	4.02858e7	+	2.33850e6i	1.19976e8			4.43423e7	+	7.68032e7i	1.98279e9	+	1.14476e9i
3.3	−321.042	−	556.060i	4845.38	+	2797.48i	−75063.3	+	130013.i	1.16215e6	−	670970.i		−	3.59243e6i	−3.78384e7	+	1.40239e7i	−7.19244e7			−1.78058e8	−	3.08406e8i	−7.46200e8	−	4.30819e8i
3.4	−171.701	−	297.394i	−22223.5	−	12830.8i	72109.8	−	124898.i	−2.79441e6	+	1.61336e6i			8.81219e6i	−2.83180e7	−	2.87490e7i	−1.39546e8			1.35547e8	+	2.34774e8i	9.59605e8	+	5.54028e8i
3.5	−83.3915	−	144.438i	27395.4	+	15816.8i	117164.	−	202934.i	1.37357e6	−	793032.i		−	5.27593e6i	1.21038e7	−	3.84956e7i	−8.28030e7			3.06630e8	+	5.31098e8i	−2.29088e8	−	1.32264e8i
3.6	−42.5283	−	73.6612i	−11566.0	−	6677.63i	127455.	−	220758.i	953531.	−	550521.i			1.13595e6i	3.51540e7	+	1.98144e7i	−4.39788e7			−1.04529e8	−	1.81049e8i	−8.11041e7	−	4.68255e7i
3.7	129.941	+	225.064i	18063.4	+	10428.9i	97302.8	−	168533.i	−2.59375e6	+	1.49750e6i			5.42057e6i	−1.11978e7	+	3.87688e7i	1.18701e8			2.38147e7	+	4.12483e7i	−6.74067e8	−	3.89173e8i
3.8	242.980	+	420.854i	2327.06	+	1343.53i	12993.1	−	22504.7i	528757.	−	305278.i			1.30581e6i	−8.77360e6	−	3.93883e7i	1.40020e8			−1.90100e8	−	3.29263e8i	2.56955e8	+	1.48353e8i
3.9	288.424	+	499.566i	−28718.7	−	16580.7i	−35305.4	+	61150.7i	1.24316e6	−	717739.i		−	1.91292e7i	−3.22982e7	+	2.41917e7i	1.10486e8			3.56131e8	+	6.16837e8i	7.17115e8	+	4.14027e8i
3.10	428.285	+	741.811i	24471.1	+	14128.4i	−235784.	+	408390.i	2.37086e6	−	1.36882e6i			2.42039e7i	−1.20363e7	+	3.85168e7i	−1.79386e8			2.05512e8	+	3.55957e8i	2.03081e9	+	1.17249e9i
3.11	447.471	+	775.042i	−7858.47	−	4537.09i	−269389.	+	466595.i	−2.15438e6	+	1.24383e6i		−	8.12086e6i	3.85394e7	−	1.19636e7i	−2.47571e8			−1.52540e8	−	2.64207e8i	−1.92805e9	−	1.11316e9i
5.1	−466.935	+	808.755i	−25633.8	+	14799.7i	−304984.	−	528248.i	1.26391e6	+	729717.i		−	2.76419e7i	3.62612e7	+	1.77070e7i	3.24822e8			2.44350e8	−	4.23226e8i	−1.18032e9	+	6.81460e8i
5.2	−409.505	+	709.284i	18896.5	−	10909.9i	−204317.	−	353887.i	−2.42095e6	−	1.39774e6i			1.78707e7i	4.02858e7	−	2.33850e6i	1.19976e8			4.43423e7	−	7.68032e7i	1.98279e9	−	1.14476e9i
5.3	−321.042	+	556.060i	4845.38	−	2797.48i	−75063.3	−	130013.i	1.16215e6	+	670970.i			3.59243e6i	−3.78384e7	−	1.40239e7i	−7.19244e7			−1.78058e8	+	3.08406e8i	−7.46200e8	+	4.30819e8i
5.4	−171.701	+	297.394i	−22223.5	+	12830.8i	72109.8	+	124898.i	−2.79441e6	−	1.61336e6i		−	8.81219e6i	−2.83180e7	+	2.87490e7i	−1.39546e8			1.35547e8	−	2.34774e8i	9.59605e8	−	5.54028e8i
5.5	−83.3915	+	144.438i	27395.4	−	15816.8i	117164.	+	202934.i	1.37357e6	+	793032.i			5.27593e6i	1.21038e7	+	3.84956e7i	−8.28030e7			3.06630e8	−	5.31098e8i	−2.29088e8	+	1.32264e8i
5.6	−42.5283	+	73.6612i	−11566.0	+	6677.63i	127455.	+	220758.i	953531.	+	550521.i		−	1.13595e6i	3.51540e7	−	1.98144e7i	−4.39788e7			−1.04529e8	+	1.81049e8i	−8.11041e7	+	4.68255e7i
5.7	129.941	−	225.064i	18063.4	−	10428.9i	97302.8	+	168533.i	−2.59375e6	−	1.49750e6i		−	5.42057e6i	−1.11978e7	−	3.87688e7i	1.18701e8			2.38147e7	−	4.12483e7i	−6.74067e8	+	3.89173e8i
5.8	242.980	−	420.854i	2327.06	−	1343.53i	12993.1	+	22504.7i	528757.	+	305278.i		−	1.30581e6i	−8.77360e6	+	3.93883e7i	1.40020e8			−1.90100e8	+	3.29263e8i	2.56955e8	−	1.48353e8i
5.9	288.424	−	499.566i	−28718.7	+	16580.7i	−35305.4	−	61150.7i	1.24316e6	+	717739.i			1.91292e7i	−3.22982e7	−	2.41917e7i	1.10486e8			3.56131e8	−	6.16837e8i	7.17115e8	−	4.14027e8i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.d	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	7.19.d.a	✓	22
7.c	even	3	1		49.19.b.a		22
7.d	odd	6	1	inner	7.19.d.a	✓	22
7.d	odd	6	1		49.19.b.a		22

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
7.19.d.a	✓	22	1.a	even	1	1	trivial
7.19.d.a	✓	22	7.d	odd	6	1	inner
49.19.b.a		22	7.c	even	3	1
49.19.b.a		22	7.d	odd	6	1

Hecke kernels

This newform subspace is the entire newspace \(S_{19}^{\mathrm{new}}(7, [\chi])\).