Space of modular forms of level 14, weight 50, and trivial character

• Label: 14.50.a
• Level: $14$
• Weight: $50$
• Character orbit: 14.a
• Rep. character: $\chi_{14}(1,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $4$
• Sturm bound: $100$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 50 \)
Character orbit:	\([\chi]\)	\(=\)	14.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(100\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{50}(\Gamma_0(14))\).

	Total	New	Old
Modular forms	100	24	76
Cusp forms	96	24	72
Eisenstein series	4	0	4

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(7\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(24\)	\(6\)	\(18\)		\(23\)	\(6\)	\(17\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)		\(26\)	\(7\)	\(19\)		\(25\)	\(7\)	\(18\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(25\)	\(6\)	\(19\)		\(24\)	\(6\)	\(18\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(25\)	\(5\)	\(20\)		\(24\)	\(5\)	\(19\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(49\)	\(11\)	\(38\)		\(47\)	\(11\)	\(36\)		\(2\)	\(0\)	\(2\)
Minus space		\(-\)		\(51\)	\(13\)	\(38\)		\(49\)	\(13\)	\(36\)		\(2\)	\(0\)	\(2\)

Trace form

24 * q - 33554432 * q^2 + 35164150554 * q^3 + 6755399441055744 * q^4 + 169831207068097674 * q^5 + 15614835231469600768 * q^6 - 9444732965739290427392 * q^8 + 2202967278581081660758700 * q^9 + 5444378866642350583578624 * q^10 - 31190411304511937543799084 * q^11 + 9897828458237151280103424 * q^12 + 884190084193616113780448382 * q^13 - 6428399400835481873502175232 * q^14 - 155354776645991215467675052120 * q^15 + 1901475900342344102245054808064 * q^16 - 1735535946451219792886391814812 * q^17 - 7066221156605616868097758593024 * q^18 - 12976797773519377535352389365938 * q^19 + 47803235054235389444991844614144 * q^20 - 166755030231745117003848547258438 * q^21 + 981643256762677683803148326535168 * q^22 + 8792138504154858832140592889116776 * q^23 + 4395185383118636667157642171383808 * q^24 + 30605912038903942365602000407539396 * q^25 + 31791121281576920857914772218183680 * q^26 - 211892103716111317035767451884544036 * q^27 - 1012357678671480407765894814141308628 * q^29 + 4586892139844205149309594241157038080 * q^30 + 16348323162479424949149207318129742620 * q^31 - 2658455991569831745807614120560689152 * q^32 - 60166939318869109175245855251919705328 * q^33 - 92537328084535293098338968536893882368 * q^34 - 75100129309840926629580686681604222534 * q^35 + 620080163432947188843412392999334707200 * q^36 + 156140648484649697364256024255635630444 * q^37 + 48911856982273697014714496895206555648 * q^38 + 3605082370839677108368431200499272538896 * q^39 + 1532456414692143338948965480836674617344 * q^40 - 5628225408637632756983568314625189775284 * q^41 - 1815569863092703269671496826918998638592 * q^42 - 5352673750810728410856954799349226729156 * q^43 - 8779320295533279247873581604848065839104 * q^44 + 8982655056597090886761195545716489868098 * q^45 - 6189362295215508339195017822008485347328 * q^46 + 243533614233852258514538667682720539343620 * q^47 + 2785991034768370339692461528031002886144 * q^48 + 880880837215059010589525064768807844531224 * q^49 - 1433877617062281820652713451870734814019584 * q^50 - 2492932202874228711241574616489639164924948 * q^51 + 248877383356191063452263430547447157358592 * q^52 + 4855497063603250903375454974181807453782752 * q^53 - 6893321625097492619530637904191967740297216 * q^54 + 26465517442385885725689300205237651306046136 * q^55 - 1809433571636962244892600015670556273672192 * q^56 + 15427783089734783180805275571011639186781996 * q^57 - 52803590375260524201206747825149873785667584 * q^58 + 9550972482444722014854372924854238049863390 * q^59 - 43728482138319542022108197290671830959390720 * q^60 + 52872380337113080252073336082772320739595802 * q^61 - 190243162322585072480784295886040120476827648 * q^62 + 240547534220244002426588485766774879987739828 * q^63 + 535217884764734955396857238543560676143529984 * q^64 + 1885474380926521420817851434748757116445065356 * q^65 - 1714742189293010313455478374729725924314447872 * q^66 - 1257368447353689978766061405851633403280321192 * q^67 - 488509940107863409934660159934275806059036672 * q^68 - 1793856464941978013093336307256427214858497312 * q^69 - 204546227558310053916864793648321866774872064 * q^70 + 6520938466112645306785899895358896387552503480 * q^71 - 1988964435487910711681733026640104898108063744 * q^72 + 16389525771591080726864743190143895286186379368 * q^73 - 6455709265150313691507454417369119313541201920 * q^74 + 7625682003672005777947406919547606866767307950 * q^75 - 3652643851080259425836439710083441384728035328 * q^76 - 12677374431361930073515472887094525425572597132 * q^77 - 75477213568376992276149380492350899426179416064 * q^78 - 79820197382784124353816456657293576016947190408 * q^79 + 13455414473584920753082437704382035986653118464 * q^80 + 345856133664439131787208391685340148556264051028 * q^81 + 202996805410184616761575149577804633736082358272 * q^82 + 449291111083227444003084887406607685199963059910 * q^83 - 46937368250865194011146519616690695047980515328 * q^84 - 1241230031753663920101338315316947920634419343052 * q^85 + 345706930189461529556231615729056075193526517760 * q^86 - 728554189005480155901501992465401014099541585708 * q^87 + 276308012835447209022164235996736753098144350208 * q^88 - 1925595778091163399753074490958943497395558669744 * q^89 + 4506513994102251762869332366732810327162007584768 * q^90 - 874807142651022603468783608579139170254495011474 * q^91 + 2474766980693850770868836770303620366005547565056 * q^92 - 4055561112070956824541317281447463893511135240440 * q^93 + 4594574487637880419843153375869799798257532010496 * q^94 + 2768316088330776179848716262871946862989948849480 * q^95 + 1237134703352333924666475177742426598535539458048 * q^96 + 10582391907414568293526716812406309543979926969732 * q^97 - 1231560673018156956117229112420023272516230316032 * q^98 - 64649504001450460098929629650031174343452322852668 * q^99

Decomposition of \(S_{50}^{\mathrm{new}}(\Gamma_0(14))\) 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					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	7
14.50.a.a	$14$	$50$	14.a	1.a	$1$	$5$	$5$	$212.893$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓	✓	✓	14.50.a.a	$1$	$1$	\(83886080\)	\(-117348111612\)	\(96\!\cdots\!50\)	\(95\!\cdots\!05\)		$-$	$-$	$+$	$2^{21}\cdot 3^{12}\cdot 5^{6}\cdot 7^{4}$	$\mathrm{SU}(2)$	\(q+2^{24}q^{2}+(-23469622322+\beta _{1}+\cdots)q^{3}+\cdots\)
14.50.a.b	$14$	$50$	14.a	1.a	$1$	$6$	$6$	$212.893$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓	✓	✓	14.50.a.b	$1$	$1$	\(-100663296\)	\(-147499349592\)	\(43\!\cdots\!60\)	\(-11\!\cdots\!06\)		$+$	$+$	$+$	$2^{38}\cdot 3^{14}\cdot 5^{6}\cdot 7^{6}\cdot 11$	$\mathrm{SU}(2)$	\(q-2^{24}q^{2}+(-24583224932-\beta _{1}+\cdots)q^{3}+\cdots\)
14.50.a.c	$14$	$50$	14.a	1.a	$1$	$6$	$6$	$212.893$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓	✓	✓	14.50.a.c	$1$	$0$	\(100663296\)	\(600288540488\)	\(23\!\cdots\!44\)	\(-11\!\cdots\!06\)		$-$	$+$	$-$	$2^{36}\cdot 3^{12}\cdot 5^{6}\cdot 7^{6}$	$\mathrm{SU}(2)$	\(q+2^{24}q^{2}+(100048090081-\beta _{1}+\cdots)q^{3}+\cdots\)
14.50.a.d	$14$	$50$	14.a	1.a	$1$	$7$	$7$	$212.893$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓	✓	14.50.a.d	$1$	$0$	\(-117440512\)	\(-300276928730\)	\(-12\!\cdots\!80\)	\(13\!\cdots\!07\)		$+$	$-$	$-$	$2^{45}\cdot 3^{14}\cdot 5^{6}\cdot 7^{9}$	$\mathrm{SU}(2)$	\(q-2^{24}q^{2}+(-42896704104-\beta _{1}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{50}^{\mathrm{old}}(\Gamma_0(14))\) into lower level spaces

\( S_{50}^{\mathrm{old}}(\Gamma_0(14)) \simeq \) \(S_{50}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{50}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{50}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)