Newform orbit 16.28.e.a

• Label: 16.28.e.a
• Level: $16$
• Weight: $28$
• Character orbit: 16.e
• Analytic conductor: $73.897$
• Analytic rank: $0$
• Dimension: $106$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	16.e (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(73.8968919741\)
Analytic rank:	\(0\)
Dimension:	\(106\)
Relative dimension:	\(53\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 106 q - 2 q^{2} - 2 q^{3} + 125095688 q^{4} - 2 q^{5} - 59499919472 q^{6} - 287180933804 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
5.1	−11581.2	+	305.932i	−2.33243e6	+	2.33243e6i	1.34031e8	−	7.08611e6i	−3.25506e9	−	3.25506e9i	2.62988e10	−	2.77259e10i		−	4.57721e11i	−1.55007e12	+	1.23070e11i		−	3.25487e12i	3.86933e13	+	3.67017e13i
5.2	−11578.9	−	382.145i	−2.39173e6	+	2.39173e6i	1.33926e8	+	8.84966e6i	1.10058e8	+	1.10058e8i	2.86077e10	−	2.67797e10i			2.84560e11i	−1.54733e12	−	1.53649e11i		−	3.81516e12i	−1.23230e12	−	1.31641e12i
5.3	−11565.4	−	677.061i	663110.	−	663110.i	1.33301e8	+	1.56610e7i	2.21940e8	+	2.21940e8i	−8.11812e9	+	7.22019e9i			2.02008e11i	−1.53108e12	−	2.71379e11i			6.74617e12i	−2.41657e12	−	2.71710e12i
5.4	−11441.8	+	1817.09i	153675.	−	153675.i	1.27614e8	−	4.15818e7i	2.87142e9	+	2.87142e9i	−1.47908e9	+	2.03757e9i		−	4.55239e11i	−1.38458e12	+	7.07660e11i			7.57837e12i	−3.80720e13	−	2.76367e13i
5.5	−11221.9	+	2878.54i	3.13170e6	−	3.13170e6i	1.17646e8	−	6.46055e7i	2.99171e9	+	2.99171e9i	−2.61290e10	+	4.41585e10i			3.77678e11i	−1.13424e12	+	1.06365e12i		−	1.19895e13i	−4.21845e13	−	2.49610e13i
5.6	−10946.6	+	3793.44i	2.44645e6	−	2.44645e6i	1.05437e8	−	8.30503e7i	−2.13207e9	−	2.13207e9i	−1.74998e10	+	3.60607e10i		−	9.04455e10i	−8.39133e11	+	1.30909e12i		−	4.34460e12i	3.14268e13	+	1.52510e13i
5.7	−10852.0	−	4056.00i	3.04255e6	−	3.04255e6i	1.01315e8	+	8.80317e7i	−1.59485e9	−	1.59485e9i	−4.53584e10	+	2.06772e10i			2.58969e10i	−7.42421e11	−	1.36626e12i		−	1.08886e13i	1.08387e13	+	2.37761e13i
5.8	−10534.4	−	4821.21i	923601.	−	923601.i	8.77296e7	+	1.01577e8i	−5.91123e8	−	5.91123e8i	−1.41825e10	+	5.27671e9i		−	1.68267e11i	−4.34455e11	−	1.49302e12i			5.91952e12i	3.37720e12	+	9.07706e12i
5.9	−9759.73	+	6242.23i	−2.84375e6	+	2.84375e6i	5.62868e7	−	1.21845e8i	1.41523e9	+	1.41523e9i	1.00029e10	−	4.55056e10i		−	4.92833e10i	2.11241e11	+	1.54053e12i		−	8.54826e12i	−2.26465e13	−	4.97807e12i
5.10	−9666.34	−	6385.89i	−1.23946e6	+	1.23946e6i	5.26586e7	+	1.23456e8i	3.17355e9	+	3.17355e9i	1.98961e10	−	4.06599e9i			1.31495e11i	2.79363e11	−	1.52964e12i			4.55307e12i	−1.04107e13	−	5.09425e13i
5.11	−9440.77	+	6714.88i	−474715.	+	474715.i	4.40386e7	−	1.26787e8i	−2.37654e9	−	2.37654e9i	1.29402e9	−	7.66932e9i			2.04420e11i	4.35602e11	+	1.49268e12i			7.17489e12i	3.83945e13	+	6.47820e12i
5.12	−9065.18	−	7213.90i	−3.30251e6	+	3.30251e6i	3.01372e7	+	1.30790e8i	3.04061e8	+	3.04061e8i	5.37618e10	−	6.11388e9i		−	2.05985e11i	6.70310e11	−	1.40305e12i		−	1.41875e13i	−5.62903e11	−	4.94983e12i
5.13	−8692.02	−	7659.41i	−956364.	+	956364.i	1.68847e7	+	1.33151e8i	−3.72252e9	−	3.72252e9i	1.56379e10	−	9.87553e8i			2.96868e11i	8.73099e11	−	1.28668e12i			5.79634e12i	3.84392e12	+	6.08685e13i
5.14	−8651.50	−	7705.14i	3.24050e6	−	3.24050e6i	1.54792e7	+	1.33322e8i	2.55225e9	+	2.55225e9i	−5.30037e10	+	3.06667e9i		−	2.23686e11i	8.93348e11	−	1.27271e12i		−	1.33761e13i	−2.41534e12	−	4.17462e13i
5.15	−8488.66	+	7884.18i	356479.	−	356479.i	9.89700e6	−	1.33852e8i	8.81914e8	+	8.81914e8i	−2.15483e8	+	5.83658e9i			2.95444e10i	9.71304e11	+	1.21426e12i			7.37144e12i	−1.44394e13	−	5.33097e11i
5.16	−6847.52	+	9345.01i	2.95774e6	−	2.95774e6i	−4.04408e7	−	1.27980e8i	6.75988e8	+	6.75988e8i	7.38694e9	+	4.78933e10i		−	3.29800e11i	1.47290e12	+	4.98428e11i		−	9.87086e12i	−1.09460e13	+	1.68828e12i
5.17	−5798.80	−	10029.5i	1.92086e6	−	1.92086e6i	−6.69655e7	+	1.16319e8i	4.80331e8	+	4.80331e8i	−3.04040e10	−	8.12664e9i			4.11420e11i	1.55494e12	−	2.87564e9i			2.46204e11i	2.03215e12	−	7.60284e12i
5.18	−5041.21	−	10430.9i	−329571.	+	329571.i	−8.33902e7	+	1.05169e8i	−2.69387e8	−	2.69387e8i	5.09916e9	+	1.77629e9i		−	2.71695e11i	1.51739e12	+	3.39659e11i			7.40836e12i	−1.45192e12	+	4.16799e12i
5.19	−4635.48	+	10617.4i	631535.	−	631535.i	−9.12424e7	−	9.84339e7i	2.52651e9	+	2.52651e9i	3.77782e9	+	9.63275e9i			3.51372e11i	1.46807e12	−	5.12473e11i			6.82793e12i	−3.85367e13	+	1.51135e13i
5.20	−4567.90	+	10646.7i	−1.19622e6	+	1.19622e6i	−9.24863e7	−	9.72661e7i	−1.71680e9	−	1.71680e9i	−7.27159e9	−	1.82001e10i		−	4.18265e11i	1.45803e12	−	5.40371e11i			4.76369e12i	2.61205e13	−	1.04361e13i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	16.28.e.a	✓	106
16.e	even	4	1	inner	16.28.e.a	✓	106

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
16.28.e.a	✓	106	1.a	even	1	1	trivial
16.28.e.a	✓	106	16.e	even	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{28}^{\mathrm{new}}(16, [\chi])\).