Newform orbit 74.8.c.b

• Label: 74.8.c.b
• Level: $74$
• Weight: $8$
• Character orbit: 74.c
• Analytic conductor: $23.116$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $2$

Newspace parameters

Level:	$N$	$=$	$74 = 2 \cdot 37$
Weight:	$k$	$=$	$8$
Character orbit:	$[\chi]$	$=$	74.c (of order $3$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$23.1164918858$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ 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.

$\operatorname{Tr}(f)(q) =$ 24 * q + 96 * q^2 + 40 * q^3 - 768 * q^4 - 136 * q^5 + 640 * q^6 + 536 * q^7 - 12288 * q^8 - 12014 * q^9 - 2176 * q^10 - 3448 * q^11 + 2560 * q^12 + 186 * q^13 + 8576 * q^14 + 10628 * q^15 - 49152 * q^16 - 1212 * q^17 + 96112 * q^18 + 15980 * q^19 - 8704 * q^20 + 6994 * q^21 - 13792 * q^22 - 62464 * q^23 - 20480 * q^24 - 48368 * q^25 + 2976 * q^26 - 323648 * q^27 + 34304 * q^28 + 200084 * q^29 - 85024 * q^30 + 609672 * q^31 + 393216 * q^32 + 131560 * q^33 + 9696 * q^34 + 43132 * q^35 + 1537792 * q^36 - 557790 * q^37 + 255680 * q^38 - 694460 * q^39 + 69632 * q^40 + 377724 * q^41 - 55952 * q^42 - 304456 * q^43 + 110336 * q^44 + 3686244 * q^45 - 249856 * q^46 - 2156696 * q^47 - 327680 * q^48 - 2929078 * q^49 + 386944 * q^50 + 968912 * q^51 + 11904 * q^52 + 2071746 * q^53 - 1294592 * q^54 - 2492580 * q^55 - 274432 * q^56 - 1669714 * q^57 + 800336 * q^58 + 479512 * q^59 - 1360384 * q^60 + 6713104 * q^61 + 2438688 * q^62 - 7785864 * q^63 + 6291456 * q^64 + 6788906 * q^65 + 2104960 * q^66 + 1823780 * q^67 + 155136 * q^68 - 3604080 * q^69 - 345056 * q^70 - 3510960 * q^71 + 6151168 * q^72 - 27590128 * q^73 + 5276496 * q^74 - 16709392 * q^75 + 1022720 * q^76 - 65144 * q^77 + 5555680 * q^78 + 1130192 * q^79 + 1114112 * q^80 - 10442988 * q^81 + 6043584 * q^82 - 3888560 * q^83 - 895232 * q^84 + 8161728 * q^85 - 1217824 * q^86 - 17683256 * q^87 + 1765376 * q^88 - 14427556 * q^89 + 14744976 * q^90 + 3386000 * q^91 + 1998848 * q^92 - 20025152 * q^93 - 8626784 * q^94 + 21486568 * q^95 - 1310720 * q^96 - 11913436 * q^97 + 23432624 * q^98 + 16388620 * q^99

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	$a_{2}$			$a_{3}$			$a_{4}$			$a_{5}$			$a_{6}$			$a_{7}$			$a_{8}$			$a_{9}$			$a_{10}$
47.1	4.00000	−	6.92820i	−42.3772	−	73.3994i	−32.0000	−	55.4256i	46.6582	+	80.8144i	−678.035			−404.125	−	699.965i	−512.000			−2498.15	+	4326.92i	746.531
47.2	4.00000	−	6.92820i	−35.3899	−	61.2970i	−32.0000	−	55.4256i	−144.990	−	251.131i	−566.238			577.803	+	1000.78i	−512.000			−1411.38	+	2444.59i	−2319.84
47.3	4.00000	−	6.92820i	−27.0658	−	46.8793i	−32.0000	−	55.4256i	61.0458	+	105.734i	−433.053			612.092	+	1060.17i	−512.000			−371.614	+	643.655i	976.733
47.4	4.00000	−	6.92820i	−17.1122	−	29.6391i	−32.0000	−	55.4256i	219.368	+	379.957i	−273.795			−84.9006	−	147.052i	−512.000			507.848	−	879.619i	3509.89
47.5	4.00000	−	6.92820i	−15.9241	−	27.5813i	−32.0000	−	55.4256i	−188.831	−	327.065i	−254.785			−701.348	−	1214.77i	−512.000			586.348	−	1015.58i	−3021.29
47.6	4.00000	−	6.92820i	1.38293	+	2.39530i	−32.0000	−	55.4256i	−125.036	−	216.569i	22.1268			133.402	+	231.058i	−512.000			1089.68	−	1887.37i	−2000.58
47.7	4.00000	−	6.92820i	7.34337	+	12.7191i	−32.0000	−	55.4256i	179.527	+	310.950i	117.494			−211.144	−	365.712i	−512.000			985.650	−	1707.20i	2872.43
47.8	4.00000	−	6.92820i	8.02885	+	13.9064i	−32.0000	−	55.4256i	−60.7750	−	105.265i	128.462			462.740	+	801.489i	−512.000			964.575	−	1670.69i	−972.400
47.9	4.00000	−	6.92820i	27.4375	+	47.5231i	−32.0000	−	55.4256i	8.21796	+	14.2339i	439.000			−392.558	−	679.931i	−512.000			−412.133	+	713.835i	131.487
47.10	4.00000	−	6.92820i	34.1855	+	59.2110i	−32.0000	−	55.4256i	13.0513	+	22.6056i	546.968			−837.864	−	1451.22i	−512.000			−1243.79	+	2154.31i	208.821
47.11	4.00000	−	6.92820i	35.4964	+	61.4816i	−32.0000	−	55.4256i	163.203	+	282.676i	567.942			755.643	+	1308.81i	−512.000			−1426.49	+	2470.75i	2611.25
47.12	4.00000	−	6.92820i	43.9945	+	76.2007i	−32.0000	−	55.4256i	−239.439	−	414.721i	703.912			358.261	+	620.527i	−512.000			−2777.54	+	4810.83i	−3831.03
63.1	4.00000	+	6.92820i	−42.3772	+	73.3994i	−32.0000	+	55.4256i	46.6582	−	80.8144i	−678.035			−404.125	+	699.965i	−512.000			−2498.15	−	4326.92i	746.531
63.2	4.00000	+	6.92820i	−35.3899	+	61.2970i	−32.0000	+	55.4256i	−144.990	+	251.131i	−566.238			577.803	−	1000.78i	−512.000			−1411.38	−	2444.59i	−2319.84
63.3	4.00000	+	6.92820i	−27.0658	+	46.8793i	−32.0000	+	55.4256i	61.0458	−	105.734i	−433.053			612.092	−	1060.17i	−512.000			−371.614	−	643.655i	976.733
63.4	4.00000	+	6.92820i	−17.1122	+	29.6391i	−32.0000	+	55.4256i	219.368	−	379.957i	−273.795			−84.9006	+	147.052i	−512.000			507.848	+	879.619i	3509.89
63.5	4.00000	+	6.92820i	−15.9241	+	27.5813i	−32.0000	+	55.4256i	−188.831	+	327.065i	−254.785			−701.348	+	1214.77i	−512.000			586.348	+	1015.58i	−3021.29
63.6	4.00000	+	6.92820i	1.38293	−	2.39530i	−32.0000	+	55.4256i	−125.036	+	216.569i	22.1268			133.402	−	231.058i	−512.000			1089.68	+	1887.37i	−2000.58
63.7	4.00000	+	6.92820i	7.34337	−	12.7191i	−32.0000	+	55.4256i	179.527	−	310.950i	117.494			−211.144	+	365.712i	−512.000			985.650	+	1707.20i	2872.43
63.8	4.00000	+	6.92820i	8.02885	−	13.9064i	−32.0000	+	55.4256i	−60.7750	+	105.265i	128.462			462.740	−	801.489i	−512.000			964.575	+	1670.69i	−972.400

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	74.8.c.b	✓	24
37.c	even	3	1	inner	74.8.c.b	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
74.8.c.b	✓	24	1.a	even	1	1	trivial
74.8.c.b	✓	24	37.c	even	3	1	inner