LMFDB - Space of modular forms of level 14, weight 48, and Character 14.c

Defining parameters

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 48 $
Character orbit:	$[\chi]$	$=$	14.c (of order $3$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$ 7 $
Character field:			$\Q(\zeta_{3})$
Newform subspaces:			$ 2 $
Sturm bound:			$96$
Trace bound:			$2$

Dimensions

The following table gives the dimensions of various subspaces of $M_{48}(14, [\chi])$.

	Total	New	Old
Modular forms	192	64	128
Cusp forms	184	64	120
Eisenstein series	8	0	8

Trace form

$ 64 q - 22\!\cdots\!48 q^{4} + 33\!\cdots\!52 q^{5} - 10\!\cdots\!52 q^{6} + 87\!\cdots\!80 q^{7} - 27\!\cdots\!12 q^{9} + 13\!\cdots\!92 q^{10} - 14\!\cdots\!36 q^{11} - 58\!\cdots\!40 q^{13} - 90\!\cdots\!36 q^{14}+ \cdots - 31\!\cdots\!44 q^{99}+O(q^{100}) $

64 * q - 2251799813685248 * q^4 + 33287336577980352 * q^5 - 1050316922580631552 * q^6 + 87004072083103998880 * q^7 - 278937453554798754948512 * q^9 + 13896588165667557998592 * q^10 - 1465686252434396802123936 * q^11 - 583278089504193855856786240 * q^13 - 907075116450351429489524736 * q^14 - 600353101923779473430258624 * q^15 - 158456325028528675187087900672 * q^16 - 89879266925473835745685209600 * q^17 - 215925538141117423976856944640 * q^18 + 2480238550708518372234033135200 * q^19 - 4684776144023393585416378515456 * q^20 - 65885004110765321814275827359968 * q^21 + 25488672572275082268431068692480 * q^22 + 203712307552166441960326168990080 * q^23 + 36954741415273893387188006027264 * q^24 - 3923488799208710935804217822776640 * q^25 + 2611427239516928158208692485881856 * q^26 + 17325854246182445687326709546112960 * q^27 + 11265523056233007979487475458375680 * q^28 + 48824559479915959085940627038532672 * q^29 + 35221266066629844277645898495819776 * q^30 + 251562178144514320531847370511404704 * q^31 + 1674935970115489738984564782750420320 * q^33 - 1671888203825020519259535100210053120 * q^34 - 103806470737219473863802731093351904 * q^35 + 39256956621533334613700680216200871936 * q^36 - 5537970331491286175606619124438779040 * q^37 + 15424359813272310671804506791707934720 * q^38 - 9919723339094542143032755743713536160 * q^39 + 977885457572213417773233832709849088 * q^40 + 319651244378967707528231684867860079424 * q^41 - 197460441894664243647545494593632993280 * q^42 - 1385780240953284685754141836383844061440 * q^43 - 103138500942275127715582582108930965504 * q^44 + 2757384443591659361464067399784882059744 * q^45 - 1007160860155581673852738666475632459776 * q^46 + 7439604438798613430600456463224539799520 * q^47 + 12842716385912191244056455467028562456384 * q^49 - 17184426965134665382602241193911938711552 * q^50 - 16167896596302210497985102301740287426080 * q^51 + 20522273332378611431416094396111315271680 * q^52 - 78787859186357802551701576873610712488160 * q^53 - 39832864880714938379763515253488915316736 * q^54 + 380028992812807373299671904314112330404096 * q^55 + 70356872333587843465293130873536119832576 * q^56 - 107325645700793566048264927579900653316800 * q^57 + 242155616285503963960425915035447816355840 * q^58 - 282166288865557488582224478663069361607040 * q^59 + 21123046922770739389227513666780862087168 * q^60 - 384666844255779395110563329938134475084576 * q^61 - 4876960171195682748718771868850118648135680 * q^62 - 2357785585727695142560462775064798576254880 * q^63 + 22300745198530623141535718272648361505980416 * q^64 + 14529800029446522222724394505425470124874528 * q^65 - 3750924314220704287977909970962492141076480 * q^66 - 15941015637212003263757753909324600694145600 * q^67 - 6324691141154645505333555172850159478374400 * q^68 + 6862295169445851787455947660595787751348096 * q^69 + 35803770428345979700162573356773667690774528 * q^70 - 146060790069733953317167508360491681713695616 * q^71 - 15194408954876722690070394275418644372520960 * q^72 + 81349790143566809024776016120834370892721120 * q^73 - 149035221679615312417304608990660015071166464 * q^74 + 1035342269417688897187380376504794323745974464 * q^75 - 349062544148775699656223187725986903464345600 * q^76 + 1193676181490377178000237599894747811445742080 * q^77 - 442917328685680360388804093577405199475015680 * q^78 - 99137073218799356145006007664709219131390080 * q^79 + 164830907004202691037589735560319389916987392 * q^80 - 3787852312539802502824372920413285253124230656 * q^81 + 658216895447366616674194322060471568055664640 * q^82 + 4248436513243839622687006057173432821191079040 * q^83 + 2953507557952859722407660842327163960310104064 * q^84 - 10667974743982804214931184238578140884949158592 * q^85 - 4573800895447574040761060144215112884332527616 * q^86 + 11952572289234453871627419155354037470763724960 * q^87 - 896802939833333142803422685303038616650383360 * q^88 + 12665643075762012396236708726381868479403239712 * q^89 - 29979966915787022477126768597753207986239569920 * q^90 + 59042544425813824351715805138149256215279421632 * q^91 - 28669958511960020817290298173206133093947146240 * q^92 - 45937838742172379506611201375880970834052450080 * q^93 + 51586150997609640975909535507689761527453188096 * q^94 + 5181690995951461911287336079476873114708218176 * q^95 + 2600458744803133472449546670744367339243831296 * q^96 + 130920512111454499666736372511498244199354317760 * q^97 + 14384827919988056335430600358825251159377182720 * q^98 - 312626924432246130025196530054445500403864913344 * q^99

Decomposition of $S_{48}^{\mathrm{new}}(14, [\chi])$ 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
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
14.48.c.a	$14$	$48$	14.c	7.c	$3$	$32$	$16$	$195.871$		None		✓			14.48.c.a	$2$	$0$	$-134217728$	$31301883536$	$17\!\cdots\!88$	$10\!\cdots\!64$		$\mathrm{SU}(2)[C_{3}]$
14.48.c.b	$14$	$48$	14.c	7.c	$3$	$32$	$16$	$195.871$		None		✓			14.48.c.b	$2$	$0$	$134217728$	$-31301883536$	$15\!\cdots\!64$	$-16\!\cdots\!84$		$\mathrm{SU}(2)[C_{3}]$

Decomposition of $S_{48}^{\mathrm{old}}(14, [\chi])$ into lower level spaces

$ S_{48}^{\mathrm{old}}(14, [\chi]) \simeq $ $S_{48}^{\mathrm{new}}(7, [\chi])$$^{\oplus 2}$

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 48 \)
Character orbit:	\([\chi]\)	\(=\)	14.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(2\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{48}^{\mathrm{new}}(14, [\chi])\) into newform subspaces

Decomposition of \(S_{48}^{\mathrm{old}}(14, [\chi])\) into lower level spaces

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	14.48.c

Level	$14$
Weight	$48$
Character orbit	14.c
Rep. character	$\chi_{14}(9,\cdot)$
Character field	$\Q(\zeta_{3})$
Dimension	$64$
Newform subspaces	$2$
Sturm bound	$96$
Trace bound	$2$