Newform orbit 18.42.c.b

• Label: 18.42.c.b
• Level: $18$
• Weight: $42$
• Character orbit: 18.c
• Analytic conductor: $191.649$
• Analytic rank: $0$
• Dimension: $42$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 42 \)
Character orbit:	\([\chi]\)	\(=\)	18.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(191.649006822\)
Analytic rank:	\(0\)
Dimension:	\(42\)
Relative dimension:	\(21\) over \(\Q(\zeta_{3})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) 42 * q - 22020096 * q^2 - 5376563127 * q^3 - 23089744183296 * q^4 - 57026267983854 * q^5 + 3627013477761024 * q^6 - 43682608823010702 * q^7 + 48422703193487572992 * q^8 + 80275085934709125369 * q^9

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
7.1	−524288.	+	908093.i	−6.03926e9	+	1.89408e7i	−5.49756e11	−	9.52205e11i	−1.32388e14	−	2.29303e14i	3.14911e15	−	5.49414e15i	1.00444e17	−	1.73974e17i	1.15292e18			3.64723e19	−	2.28776e17i	2.77638e20
7.2	−524288.	+	908093.i	−6.03769e9	−	1.38980e8i	−5.49756e11	−	9.52205e11i	1.53400e14	+	2.65696e14i	3.29169e15	−	5.40992e15i	−9.97031e16	+	1.72691e17i	1.15292e18			3.64344e19	+	1.67824e18i	−3.21703e20
7.3	−524288.	+	908093.i	−5.85214e9	+	1.49181e9i	−5.49756e11	−	9.52205e11i	−1.65929e14	−	2.87398e14i	1.71350e15	−	6.09643e15i	6.34928e16	−	1.09973e17i	1.15292e18			3.20220e19	−	1.74606e19i	3.47979e20
7.4	−524288.	+	908093.i	−5.66353e9	+	2.09701e9i	−5.49756e11	−	9.52205e11i	1.03807e14	+	1.79800e14i	1.06504e15	−	6.24245e15i	9.12153e16	−	1.57989e17i	1.15292e18			2.76781e19	−	2.37529e19i	−2.17700e20
7.5	−524288.	+	908093.i	−5.17511e9	−	3.11308e9i	−5.49756e11	−	9.52205e11i	−3.95214e13	−	6.84531e13i	5.54021e15	−	3.06733e15i	−1.87835e17	+	3.25340e17i	1.15292e18			1.70905e19	+	3.22210e19i	8.28825e19
7.6	−524288.	+	908093.i	−4.52831e9	+	3.99592e9i	−5.49756e11	−	9.52205e11i	−4.28249e13	−	7.41749e13i	−1.25453e15	−	6.20714e15i	−1.01496e17	+	1.75797e17i	1.15292e18			4.53818e18	−	3.61896e19i	8.98103e19
7.7	−524288.	+	908093.i	−3.73854e9	−	4.74303e9i	−5.49756e11	−	9.52205e11i	1.22684e14	+	2.12494e14i	6.26718e15	−	9.08234e14i	5.99568e16	−	1.03848e17i	1.15292e18			−8.51960e18	+	3.54640e19i	−2.57286e20
7.8	−524288.	+	908093.i	−2.46633e9	−	5.51273e9i	−5.49756e11	−	9.52205e11i	−1.35659e14	−	2.34967e14i	6.29914e15	+	6.50597e14i	1.48613e16	−	2.57406e16i	1.15292e18			−2.43074e19	+	2.71925e19i	2.84497e20
7.9	−524288.	+	908093.i	−1.64776e9	+	5.81015e9i	−5.49756e11	−	9.52205e11i	3.72247e13	+	6.44750e13i	−4.41226e15	−	4.54251e15i	1.48093e17	−	2.56505e17i	1.15292e18			−3.10428e19	−	1.91475e19i	−7.80658e19
7.10	−524288.	+	908093.i	−1.35330e9	+	5.88571e9i	−5.49756e11	−	9.52205e11i	−1.40864e14	−	2.43983e14i	−4.63525e15	−	4.31473e15i	−1.09486e17	+	1.89635e17i	1.15292e18			−3.28101e19	−	1.59303e19i	2.95413e20
7.11	−524288.	+	908093.i	8.40890e7	+	6.03870e9i	−5.49756e11	−	9.52205e11i	1.60686e14	+	2.78317e14i	−5.52779e15	−	3.08966e15i	−5.95865e16	+	1.03207e17i	1.15292e18			−3.64589e19	+	1.01558e18i	−3.36983e20
7.12	−524288.	+	908093.i	3.47673e8	−	6.02927e9i	−5.49756e11	−	9.52205e11i	−3.28810e13	−	5.69515e13i	5.29286e15	+	3.47679e15i	−8.73758e15	+	1.51339e16i	1.15292e18			−3.62312e19	−	4.19243e18i	6.89564e19
7.13	−524288.	+	908093.i	1.47338e9	−	5.85680e9i	−5.49756e11	−	9.52205e11i	1.29292e14	+	2.23941e14i	4.54605e15	+	4.40862e15i	3.67136e16	−	6.35899e16i	1.15292e18			−3.21313e19	−	1.72586e19i	−2.71145e20
7.14	−524288.	+	908093.i	2.90157e9	+	5.29659e9i	−5.49756e11	−	9.52205e11i	−9.19168e13	−	1.59205e14i	−6.33106e15	−	1.42045e14i	6.83001e16	−	1.18299e17i	1.15292e18			−1.96348e19	+	3.07369e19i	1.92764e20
7.15	−524288.	+	908093.i	3.65385e9	−	4.80858e9i	−5.49756e11	−	9.52205e11i	2.49036e13	+	4.31343e13i	2.45097e15	+	5.83911e15i	−1.32312e17	+	2.29171e17i	1.15292e18			−9.77182e18	−	3.51396e19i	−5.22267e19
7.16	−524288.	+	908093.i	3.97642e9	+	4.54545e9i	−5.49756e11	−	9.52205e11i	8.28610e13	+	1.43520e14i	−6.21248e15	+	1.22784e15i	−1.16479e17	+	2.01747e17i	1.15292e18			−4.84917e18	+	3.61492e19i	−1.73772e20
7.17	−524288.	+	908093.i	4.23874e9	−	4.30187e9i	−5.49756e11	−	9.52205e11i	−1.27772e14	−	2.21308e14i	1.68417e15	+	6.10459e15i	1.95491e17	−	3.38600e17i	1.15292e18			−5.39103e17	−	3.64690e19i	2.67957e20
7.18	−524288.	+	908093.i	5.46332e9	−	2.57394e9i	−5.49756e11	−	9.52205e11i	1.96886e14	+	3.41016e14i	−5.26975e14	+	6.31069e15i	1.26420e17	−	2.18967e17i	1.15292e18			2.32227e19	−	2.81245e19i	−4.12899e20
7.19	−524288.	+	908093.i	5.68489e9	+	2.03839e9i	−5.49756e11	−	9.52205e11i	−3.40036e13	−	5.88960e13i	−4.83157e15	+	4.09370e15i	1.02131e17	−	1.76896e17i	1.15292e18			2.81629e19	+	2.31761e19i	7.13108e19
7.20	−524288.	+	908093.i	5.96222e9	−	9.61756e8i	−5.49756e11	−	9.52205e11i	−1.88834e14	−	3.27070e14i	−2.25255e15	+	5.91849e15i	−1.39263e17	+	2.41211e17i	1.15292e18			3.46230e19	−	1.14684e19i	3.96013e20

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
9.c	even	3	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	18.42.c.b	✓	42
9.c	even	3	1	inner	18.42.c.b	✓	42

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
18.42.c.b	✓	42	1.a	even	1	1	trivial
18.42.c.b	✓	42	9.c	even	3	1	inner