LMFDB - Space of modular forms of level 1, weight 54, and trivial character

Defining parameters

Level:	$N$	$=$	$1$
Weight:	$k$	$=$	$54$
Character orbit:	$[\chi]$	$=$	1.a (trivial)
Character field:			$\Q$
Newform subspaces:			$1$
Sturm bound:			$4$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{54}(\Gamma_0(1))$ .

	Total	New
Modular forms	5	5
Cusp forms	4	4
Eisenstein series	1	1

Trace form

4 q - 68476320 q^{2} - 1048411007280 q^{3} + 78\!\cdots\!28 q^{4} - 45\!\cdots\!00 q^{5} + 36\!\cdots\!28 q^{6} - 22\!\cdots\!00 q^{7} + 13\!\cdots\!40 q^{8} + 11\!\cdots\!12 q^{9} + 23\!\cdots\!00 q^{10}+ \cdots + 20\!\cdots\!84 q^{99}+O(q^{100})

4 * q - 68476320 * q^2 - 1048411007280 * q^3 + 7829639419798528 * q^4 - 4563895793294313000 * q^5 + 365243285516994476928 * q^6 - 224841770748445429600 * q^7 + 139144349902380051824640 * q^8 + 11374560253581116395684212 * q^9 + 239691034935725362703784000 * q^10 + 2482225436399137396212828528 * q^11 - 36954074065409878778429091840 * q^12 + 38846785417115118418757458040 * q^13 - 2318389217831653006768429089024 * q^14 + 10885572770546350531014554412000 * q^15 - 158675761303426594387641091751936 * q^16 - 869470789827683332623267869375160 * q^17 - 6763457530054882037574097250222880 * q^18 - 25573430606481293737377136094590960 * q^19 - 137124186244908431721319713321216000 * q^20 - 456430072728043514442750337944104832 * q^21 - 930239272324579210970924539473171840 * q^22 + 692283403499940921426611559815316960 * q^23 + 8087484160806183674287697801240248320 * q^24 + 36481255519181820020535795184467437500 * q^25 + 88199592302469577023283184091414497088 * q^26 + 85289145712610214901983766257673297440 * q^27 - 5693966184427848677134093343909109760 * q^28 - 1403448065249545071892827367228561632840 * q^29 - 5799093432823921615312476874120821216000 * q^30 - 3964172885133396823441211087460727887232 * q^31 + 3478175004061909463146496356345215713280 * q^32 + 26488618539649572306469337360654123586240 * q^33 + 149997773608319010417738024908146242937536 * q^34 + 61365948170559642529868826584708753304000 * q^35 + 74373890656883085418751005021443502838784 * q^36 - 283737807523680188930907412534612515795880 * q^37 - 2149858349100743242412726210681586741479040 * q^38 - 3695759405159081384443679869760359201600416 * q^39 - 530824655589569872286083924732862423040000 * q^40 + 816268439352205816307560932682632884757288 * q^41 + 34473336675516302350057635130637873086909440 * q^42 + 45680017888765970285202819125021276867644400 * q^43 + 36450257868828743991533939202628376274333696 * q^44 - 52785302554790432865174172783106255610789000 * q^45 - 286598377899888278123152881845505043619242752 * q^46 - 450331332464449690190061856166374876708223040 * q^47 - 307327868606734954261884348178650744005591040 * q^48 + 61256589204322440136838991964906594854806628 * q^49 + 521470775015683964723409941128468604170500000 * q^50 + 4823104417223604238685131462744139603812556448 * q^51 + 6480873745173555872757727943119261362842777600 * q^52 + 3894630980633224571473003534722579109607488920 * q^53 - 9094643349894867160783307676594158361928776960 * q^54 - 25220087960941681699071033843031097345513916000 * q^55 - 41708301235969326798480993683317763265335132160 * q^56 - 78794438935790744156133212572387836678302205120 * q^57 + 23153390818000102952173078969301145284748805440 * q^58 + 161352440713620380366889082872890081870684067120 * q^59 + 406305479737925709888509415210821103661353984000 * q^60 + 65647964430669998286897420448040378258467279928 * q^61 + 397783228528983419561799088374192602352940661760 * q^62 - 302986559547633524951279897150694105228921738720 * q^63 - 1033735951572319175631379922707833053066697900032 * q^64 - 3420620126550512806970332375686936386825214798000 * q^65 - 658347942888276364671353073747068107649649237504 * q^66 - 1114206317023626852397290701407230552884994982960 * q^67 + 2848472333882807118405541680155589548651324344320 * q^68 + 775291276168249766930956334518267852448076104064 * q^69 + 33179725699094578918821931009364962909309028928000 * q^70 + 3568565136657140046536067623675232742954247775648 * q^71 + 26402495617891679740981292232213348882933665464320 * q^72 - 70697396612705842206652346649767546611106446705240 * q^73 - 2477665041456578897595255396512213772982320606144 * q^74 - 214147644415917420957952976584023331338227237250000 * q^75 + 45189859364823457604586927205450004182295006842880 * q^76 - 161023821416166064076421008340115759390173471196800 * q^77 + 512081797195935502825354508308769411884974336211200 * q^78 - 156417020870005797258130007144678737115075518344640 * q^79 + 1135588155590291950317639086884448883835074772992000 * q^80 - 498743339483968532647094896032944674900788125971356 * q^81 + 1595344511843776298585510858680959074676233895092160 * q^82 - 2616078236644862619515249170129703738064518568891120 * q^83 - 769036580140824400081375315496419857132807898497024 * q^84 - 2322985242765977498040783878693923846942012787106000 * q^85 - 771473689440649042704510533443081756253708267624832 * q^86 - 4553516071908987502170780484180858967295593004331680 * q^87 + 5676678682320308097974311975312643702936459537940480 * q^88 - 377838445322199523132380916699165405584669879895320 * q^89 + 20963916598038401334962666668658272688885372614152000 * q^90 + 12668228612190081366491587480915595422042752342094528 * q^91 + 8910978937854086377493208678167975007758313267978240 * q^92 - 9941509412818307372855389204673554966584205049372160 * q^93 - 37159704993639903541096652460057479885138542709712384 * q^94 - 17088387525725080516970439013001314242158750454180000 * q^95 - 115890361493294838169648124263288994270902966699425792 * q^96 + 10362822344952442405677621761316902058987153293434760 * q^97 - 88214006056362955165305640276151180685109758813947040 * q^98 + 200357011548750056817277275156798035565052172823063984 * q^99

Decomposition of $S_{54}^{\mathrm{new}}(\Gamma_0(1))$ 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				Fricke sign	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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$ -expansion
1.54.a.a	$1$	$54$	1.a	1.a	$1$	$4$	$4$	$17.790$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	✓	✓	✓	1.54.a.a	$1$	$1$	$-68476320$	$-10\!\cdots\!80$	$-45\!\cdots\!00$	$-22\!\cdots\!00$	$+$	$2^{27}\cdot 3^{8}\cdot 5^{3}\cdot 7\cdot 13$	$\mathrm{SU}(2)$	$q+(-17119080+\beta _{1})q^{2}+(-262102751820+\cdots)q^{3}+\cdots$

Overview	Random
Universe	Knowledge

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

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Defining parameters

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Trace form

Decomposition of $S_{54}^{\mathrm{new}}(\Gamma_0(1))$ into newform subspaces

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	1.54.a

Level	$1$
Weight	$54$
Character orbit	1.a
Rep. character	$\chi_{1}(1,\cdot)$
Character field	$\Q$
Dimension	$4$
Newform subspaces	$1$
Sturm bound	$4$
Trace bound	$0$

Properties

Related objects

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Defining parameters

Dimensions

Decomposition of S54new(Γ0(1))S_{54}^{\mathrm{new}}(\Gamma_0(1))S54new​(Γ0​(1)) into newform subspaces

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

Decomposition of $S_{54}^{\mathrm{new}}(\Gamma_0(1))$ into newform subspaces