Space of modular forms of level 7, weight 48, and Character 7.c

• Label: 7.48.c
• Level: $7$
• Weight: $48$
• Character orbit: 7.c
• Rep. character: $\chi_{7}(2,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $60$
• Newform subspaces: $1$
• Sturm bound: $32$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 48 \)
Character orbit:	\([\chi]\)	\(=\)	7.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(32\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{48}(7, [\chi])\).

	Total	New	Old
Modular forms	64	64	0
Cusp forms	60	60	0
Eisenstein series	4	4	0

Trace form

60 * q + 2603046 * q^2 - 94143178828 * q^3 - 1911222542908572 * q^4 - 28564597244068302 * q^5 + 1050598397557342204 * q^6 - 31886901785147812368 * q^7 + 2938640258192802114192 * q^8 - 261990800242973120942404 * q^9 - 125544353489015919977574 * q^10 - 731794915318088024727972 * q^11 + 15778811189943207537454204 * q^12 + 166351921827064152053992488 * q^13 + 2596702913459481945275749326 * q^14 + 7210246202197010042754803888 * q^15 - 118432764218917496411452705968 * q^16 + 10453289122064389194211554126 * q^17 + 226977214575340425189470755108 * q^18 - 2395238990553797395003751610972 * q^19 + 17588143511591301532150326785544 * q^20 + 44040175306626773276737710045574 * q^21 - 68920069263484486396594219250868 * q^22 - 83572619323630138438170499657608 * q^23 - 1034996536235867473532593097992824 * q^24 - 5004819735904630033056050574181584 * q^25 - 697617350083098029487053553454164 * q^26 + 2850273854661055495678682794344056 * q^27 - 35708695574554837329669210660626772 * q^28 - 5918271274964422216583040768659736 * q^29 + 72021232817317421403012686996315422 * q^30 - 271683924402661828370866001013563424 * q^31 - 768982745569217543438176929868772832 * q^32 - 608408389087481474352450603921013222 * q^33 + 6610183811909199294801405148056226428 * q^34 + 2305602268401163447148139883969365804 * q^35 + 41157082813035443006713496615261344336 * q^36 + 250394546453878388915889082385892786 * q^37 + 22945446449813323619795552581589121006 * q^38 + 10683535896400202055917873319828250328 * q^39 + 24590715699354778576653559847432908488 * q^40 - 180932094954659826083705451375788215464 * q^41 - 266928115452044292180717706350126835576 * q^42 + 400305034600210831179684466889504003568 * q^43 + 37084934012258205007543597482381889164 * q^44 - 1940240126992616075151708263297117076244 * q^45 + 84222092082007806742402587671195813310 * q^46 - 8459013562249323373960288231499432968464 * q^47 + 18073290962039336024912706740181212423200 * q^48 - 23694565677690927280837453729284485605476 * q^49 + 52767760710019199251050866540148318688656 * q^50 + 37286228790548333906890160283885584842236 * q^51 - 101125876048597913639320646791708568515512 * q^52 + 58826785559391072280065614144367325753602 * q^53 + 36392687285710762974931410552074980539190 * q^54 - 194207367451089409268986103342032404746880 * q^55 + 264971541296790337128033932556476697237408 * q^56 + 204650063942278732037509609137104826542756 * q^57 + 744055058511297186944291317307839280276700 * q^58 + 281005188801642680201399939540478641404908 * q^59 - 2289336755209705926790869033601438300688924 * q^60 + 1437391748801582168923090922870033400389322 * q^61 + 4945024594323884317257900961714066847350092 * q^62 + 5927616880798426343016197722001153759956024 * q^63 - 3852177629696792737624681140463703952870528 * q^64 - 7913885297583636740702238937185561682725492 * q^65 - 958913415598479804432731616046620511987826 * q^66 + 11042320939300470574342167117175728963267636 * q^67 - 16442319591533585045195961345380895740142516 * q^68 - 100680764970545323928872197408546274864610196 * q^69 - 126435535345633931184698366920530653242713210 * q^70 + 138825767694856614679788972073918019980993440 * q^71 + 99719279039006090165851253449715301044524176 * q^72 - 131257404207638740819179289691808952406672538 * q^73 + 370702588816074696496390950909335590534884402 * q^74 - 891846930545456185903532802122995971631324088 * q^75 + 1291644237976561085859922166690760995195645496 * q^76 - 996402568796040824888136067558521708770413554 * q^77 + 3318437053246600127527535537995338570321971896 * q^78 + 315185642043838687878691644863201614098553200 * q^79 - 2661538505163426457980896788009537782431924688 * q^80 + 169351233780191746717440232586712008393871938 * q^81 - 3847705900709962955788430966160213225719018988 * q^82 - 592966603828932384331725036350164582435978992 * q^83 - 12303966087733734512184261957872329783103878948 * q^84 + 13411279215195503976249995806509140574142135236 * q^85 + 1990218897949335167672814596096309600447739384 * q^86 - 11149532262910626716338990750466650761000746920 * q^87 + 18809484368967539179803915037796426750641270056 * q^88 - 18694314174597900092034427470183353387667000522 * q^89 + 41739481118309810180490378193031975420473277896 * q^90 - 27310888947835301254089327510476521990876272480 * q^91 + 128968307831731056553884318802962411841348701624 * q^92 + 58157394258369612703146178463318826334439356158 * q^93 - 49977757391769923254763003429852355746885781978 * q^94 + 48315454740952071485257561655753745173623939152 * q^95 - 306355671823254887581348683430096341446453405344 * q^96 + 55769560154838989062526943910146341250337456824 * q^97 - 265420296862922693401804908396492267236583896034 * q^98 + 320431906845171076644797946878716034141517119456 * q^99

Decomposition of \(S_{48}^{\mathrm{new}}(7, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
7.48.c.a	$7$	$48$	7.c	7.c	$3$	$60$	$30$	$97.935$		None		✓	✓	✓	7.48.c.a	$2$	$0$	\(2603046\)	\(-94143178828\)	\(-28\!\cdots\!02\)	\(-31\!\cdots\!68\)		$\mathrm{SU}(2)[C_{3}]$