Newform orbit 79.10.g.a

• Label: 79.10.g.a
• Level: $79$
• Weight: $10$
• Character orbit: 79.g
• Analytic conductor: $40.688$
• Analytic rank: $0$
• Dimension: $1416$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 79 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	79.g (of order \(39\), degree \(24\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(40.6878310569\)
Analytic rank:	\(0\)
Dimension:	\(1416\)
Relative dimension:	\(59\) over \(\Q(\zeta_{39})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1416 q - 42 q^{2} - 187 q^{3} + 15592 q^{4} - 25 q^{5} - 9797 q^{6} - 11187 q^{7} - 129906 q^{8} + 374800 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2.1	−34.7971	−	26.1483i	194.623	+	31.6293i	384.654	+	1327.98i	618.620	+	391.192i	−5945.24	−	6189.65i	5663.76	−	6936.84i	13437.0	−	35430.5i	18207.5	+	6078.56i	−11297.2	−	29788.2i
2.2	−34.2619	−	25.7461i	9.33095	+	1.51643i	368.566	+	1272.44i	−1327.98	−	839.761i	−280.654	−	292.191i	−5331.48	+	6529.88i	12351.5	−	32568.2i	−18585.3	−	6204.68i	23878.3	+	62962.0i
2.3	−33.7618	−	25.3703i	14.1793	+	2.30436i	353.757	+	1221.31i	188.203	+	119.013i	−420.256	−	437.533i	−990.711	+	1213.40i	11374.1	−	29991.0i	−18474.3	−	6167.63i	−3334.69	−	8792.86i
2.4	−32.3714	−	24.3255i	−168.301	−	27.3516i	313.729	+	1083.12i	1206.71	+	763.074i	4782.81	+	4979.43i	3800.94	−	4655.30i	8839.86	−	23308.8i	8907.15	+	2973.64i	−20500.6	−	54055.5i
2.5	−31.7378	−	23.8494i	−262.049	−	42.5870i	296.048	+	1022.07i	−950.407	−	601.001i	7301.18	+	7601.33i	−4491.44	+	5501.01i	7772.17	−	20493.5i	48185.8	+	16086.8i	15830.3	+	41741.1i
2.6	−31.1548	−	23.4113i	−107.350	−	17.4460i	280.084	+	966.961i	−2207.23	−	1395.77i	2936.03	+	3056.73i	7616.51	−	9328.53i	6836.45	−	18026.2i	−7450.42	−	2487.31i	36089.0	+	95158.8i
2.7	−29.6615	−	22.2892i	−92.2744	−	14.9960i	240.551	+	830.479i	1556.38	+	984.193i	2402.75	+	2501.53i	−4646.23	+	5690.60i	4639.31	−	12232.9i	−10380.4	−	3465.47i	−24227.7	−	63883.1i
2.8	−28.5371	−	21.4443i	217.300	+	35.3147i	212.064	+	732.129i	−1838.11	−	1162.35i	−5443.83	−	5667.62i	−822.056	+	1006.84i	3167.34	−	8351.59i	27302.3	+	9114.84i	27528.7	+	72587.2i
2.9	−28.2476	−	21.2267i	188.136	+	30.5750i	204.908	+	707.424i	758.495	+	479.643i	−4665.38	−	4857.17i	−3191.76	+	3909.19i	2812.94	−	7417.10i	15790.1	+	5271.51i	−11244.4	−	29649.1i
2.10	−27.6981	−	20.8138i	176.084	+	28.6164i	191.525	+	661.222i	2033.18	+	1285.71i	−4281.58	−	4457.59i	−4427.51	+	5422.71i	2167.25	−	5714.58i	11516.5	+	3844.78i	−29554.9	−	77929.9i
2.11	−25.7015	−	19.3134i	16.4979	+	2.68117i	145.112	+	500.985i	−184.689	−	116.790i	−372.239	−	387.542i	3836.14	−	4698.42i	109.193	−	287.919i	−18405.0	−	6144.51i	2491.17	+	6568.68i
2.12	−24.1279	−	18.1310i	85.9503	+	13.9683i	110.978	+	383.140i	−444.414	−	281.030i	−1820.54	−	1895.39i	1041.58	−	1275.70i	−1210.55	+	3191.96i	−11477.7	−	3831.82i	5627.44	+	14838.3i
2.13	−22.1905	−	16.6751i	−139.253	−	22.6308i	71.9125	+	248.271i	−1050.95	−	664.581i	2712.72	+	2824.24i	−1777.94	+	2177.58i	−2495.42	+	6579.88i	209.130	+	69.8179i	12239.2	+	32272.1i
2.14	−22.1095	−	16.6142i	−188.711	−	30.6686i	70.3506	+	242.878i	−155.711	−	98.4660i	3662.78	+	3813.36i	1088.43	−	1333.08i	−2541.37	+	6701.04i	16001.4	+	5342.05i	1806.77	+	4764.06i
2.15	−20.9593	−	15.7499i	61.8491	+	10.0515i	48.7865	+	168.431i	1976.19	+	1249.66i	−1138.01	−	1184.79i	7094.80	−	8689.56i	−3129.74	+	8252.45i	−14945.8	−	4989.63i	−21737.4	−	57316.9i
2.16	−17.5392	−	13.1799i	−2.41776	−	0.392924i	−8.53164	−	29.4547i	−1382.33	−	874.134i	37.2270	+	38.7574i	−7848.83	+	9613.07i	−4221.83	+	11132.0i	−18664.4	−	6231.08i	12724.1	+	33550.6i
2.17	−16.7375	−	12.5774i	−171.045	−	27.7976i	−20.4948	−	70.7562i	1791.60	+	1132.94i	2513.25	+	2616.57i	−4936.30	+	6045.87i	−4348.07	+	11464.9i	9813.75	+	3276.31i	−15737.5	−	41496.3i
2.18	−15.9618	−	11.9945i	−26.5108	−	4.30843i	−31.5361	−	108.875i	1377.65	+	871.171i	371.484	+	386.756i	804.916	−	985.843i	−4427.55	+	11674.5i	−17985.8	−	6004.54i	−11540.5	−	30429.8i
2.19	−15.8051	−	11.8767i	263.802	+	42.8721i	−33.7042	−	116.360i	568.111	+	359.251i	−3660.23	−	3810.71i	6804.29	−	8333.74i	−4438.70	+	11703.9i	49083.7	+	16386.5i	−4712.29	−	12425.3i
2.20	−15.0868	−	11.3370i	−270.553	−	43.9691i	−43.3637	−	149.709i	1023.15	+	647.004i	3583.29	+	3730.60i	5943.85	−	7279.90i	−4469.31	+	11784.6i	52595.5	+	17558.9i	−8101.03	−	21360.7i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
79.g	even	39	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	79.10.g.a	✓	1416
79.g	even	39	1	inner	79.10.g.a	✓	1416

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
79.10.g.a	✓	1416	1.a	even	1	1	trivial
79.10.g.a	✓	1416	79.g	even	39	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{10}^{\mathrm{new}}(79, [\chi])\).