Newform orbit 28.11.g.a

• Label: 28.11.g.a
• Level: $28$
• Weight: $11$
• Character orbit: 28.g
• Analytic conductor: $17.790$
• Analytic rank: $0$
• Dimension: $76$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	28.g (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(17.7900030749\)
Analytic rank:	\(0\)
Dimension:	\(76\)
Relative dimension:	\(38\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 76 q + 10 q^{2} - 628 q^{4} - 2 q^{5} - 2052 q^{6} + 118072 q^{8} + 669220 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
11.1	−31.9896	−	0.816280i	−323.192	−	186.595i	1022.67	+	52.2249i	−1774.27	−	3073.13i	10186.4	+	6232.90i	16496.3	+	3216.50i	−32672.1	−	2505.44i	40110.7	+	69473.7i	54249.6	+	99756.3i
11.2	−31.9820	+	1.07380i	−208.922	−	120.621i	1021.69	−	68.6844i	1157.08	+	2004.13i	6811.27	+	3633.37i	−12853.9	−	10828.4i	−32602.0	+	3293.75i	−425.502	−	736.991i	−39157.8	−	62853.5i
11.3	−31.9441	+	1.89102i	223.594	+	129.092i	1016.85	−	120.814i	−1508.25	−	2612.36i	−7386.60	−	3700.90i	−3730.18	+	16387.8i	−32253.8	+	5782.17i	3804.87	+	6590.23i	53119.6	+	80597.4i
11.4	−29.2372	−	13.0071i	242.493	+	140.003i	685.633	+	760.581i	−144.627	−	250.501i	−5268.80	−	7247.44i	858.224	−	16785.1i	−10153.1	−	31155.4i	9677.46	+	16761.9i	970.206	+	9205.12i
11.5	−29.1315	−	13.2422i	−44.2451	−	25.5449i	673.291	+	771.528i	2794.40	+	4840.04i	950.657	+	1330.06i	−252.403	+	16805.1i	−9397.30	−	31391.6i	−28219.4	−	48877.5i	−17312.6	−	178002.i
11.6	−28.7595	+	14.0317i	67.6338	+	39.0484i	630.222	−	807.091i	521.080	+	902.537i	−2493.03	−	173.996i	16521.4	−	3085.27i	−6800.02	+	32054.7i	−26474.9	−	45855.9i	−27650.2	−	18644.9i
11.7	−26.5031	+	17.9328i	352.583	+	203.564i	380.832	−	950.549i	2803.34	+	4855.53i	−12995.0	+	927.705i	−16551.8	−	2917.82i	6952.70	+	32021.9i	53352.2	+	92408.7i	−161370.	−	78415.1i
11.8	−25.0505	−	19.9116i	−136.173	−	78.6198i	231.059	+	997.591i	−2579.74	−	4468.24i	1845.78	+	4680.89i	−15396.0	+	6740.69i	14075.4	−	29590.9i	−17162.4	−	29726.1i	−24345.8	+	163298.i
11.9	−23.1572	+	22.0849i	−63.6476	−	36.7470i	48.5117	−	1022.85i	−2024.99	−	3507.39i	2285.45	−	554.696i	−13123.5	−	10500.0i	21466.2	+	24757.7i	−26823.8	−	46460.2i	124354.	+	36499.5i
11.10	−22.2755	+	22.9740i	−324.557	−	187.383i	−31.6051	−	1023.51i	1018.69	+	1764.43i	11534.6	−	3282.31i	−3581.93	+	16420.9i	24218.1	+	22073.1i	40700.5	+	70495.3i	−63227.8	−	15900.1i
11.11	−21.0677	−	24.0864i	−117.708	−	67.9587i	−136.306	+	1014.89i	180.327	+	312.335i	842.955	+	4266.89i	16802.0	−	409.699i	27316.6	−	18098.2i	−20287.7	−	35139.4i	3723.95	−	10923.6i
11.12	−16.3053	−	27.5343i	393.912	+	227.425i	−492.273	+	897.911i	1045.79	+	1811.37i	−160.877	−	14554.3i	5938.56	+	15722.9i	32750.0	−	1086.36i	73920.1	+	128033.i	32822.7	−	58330.2i
11.13	−15.6927	−	27.8880i	−393.912	−	227.425i	−531.477	+	875.276i	1045.79	+	1811.37i	−160.877	+	14554.3i	−5938.56	−	15722.9i	32750.0	+	1086.36i	73920.1	+	128033.i	34104.0	−	57590.4i
11.14	−13.3831	+	29.0670i	384.560	+	222.026i	−665.786	−	778.013i	−2244.06	−	3886.82i	−11600.2	+	8206.63i	15403.6	−	6723.42i	31524.8	−	8940.21i	69066.5	+	119627.i	143011.	−	13210.4i
11.15	−11.3367	+	29.9245i	100.045	+	57.7608i	−766.957	−	678.493i	210.994	+	365.453i	−2862.65	+	2338.97i	−3014.28	+	16534.5i	28998.4	−	15259.0i	−22851.9	−	39580.6i	−13328.0	+	2170.87i
11.16	−10.3256	−	30.2883i	117.708	+	67.9587i	−810.766	+	625.488i	180.327	+	312.335i	842.955	−	4266.89i	−16802.0	+	409.699i	27316.6	+	18098.2i	−20287.7	−	35139.4i	7598.13	−	8686.83i
11.17	−7.50047	+	31.1086i	−91.7870	−	52.9933i	−911.486	−	466.658i	2237.92	+	3876.18i	2336.99	−	2457.89i	10924.9	−	12771.9i	21353.6	−	24854.9i	−23907.9	−	41409.7i	−137368.	+	40545.1i
11.18	−4.71865	−	31.6502i	136.173	+	78.6198i	−979.469	+	298.692i	−2579.74	−	4468.24i	1845.78	−	4680.89i	15396.0	−	6740.69i	14075.4	+	29590.9i	−17162.4	−	29726.1i	−129248.	+	102733.i
11.19	−3.57615	+	31.7995i	−339.446	−	195.979i	−998.422	−	227.440i	−1611.22	−	2790.72i	7445.97	−	10093.4i	9933.75	−	13557.1i	10803.0	−	30936.0i	47291.3	+	81911.0i	94505.5	−	41256.1i
11.20	3.09772	−	31.8497i	44.2451	+	25.5449i	−1004.81	−	197.323i	2794.40	+	4840.04i	950.657	−	1330.06i	252.403	−	16805.1i	−9397.30	+	31391.6i	−28219.4	−	48877.5i	162810.	−	74007.7i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
7.c	even	3	1	inner
28.g	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	28.11.g.a	✓	76
4.b	odd	2	1	inner	28.11.g.a	✓	76
7.c	even	3	1	inner	28.11.g.a	✓	76
28.g	odd	6	1	inner	28.11.g.a	✓	76

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
28.11.g.a	✓	76	1.a	even	1	1	trivial
28.11.g.a	✓	76	4.b	odd	2	1	inner
28.11.g.a	✓	76	7.c	even	3	1	inner
28.11.g.a	✓	76	28.g	odd	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{11}^{\mathrm{new}}(28, [\chi])\).