Properties

Label 4.34
Level 4
Weight 34
Dimension 3
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 34
Trace bound 0

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Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 34 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(34\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{34}(\Gamma_1(4))\).

Total New Old
Modular forms 18 3 15
Cusp forms 15 3 12
Eisenstein series 3 0 3

Trace form

\( 3q + 92491788q^{3} - 53880683886q^{5} + 4541009914392q^{7} + 6032364433690023q^{9} + O(q^{10}) \) \( 3q + 92491788q^{3} - 53880683886q^{5} + 4541009914392q^{7} + 6032364433690023q^{9} + 227617657302449700q^{11} + 272970442217358762q^{13} - 32142473481241105848q^{15} + 93037188311816716854q^{17} + 1324887806175081735228q^{19} - 2289418149258037352352q^{21} + 11680621362017694733896q^{23} + 258183723295544823174621q^{25} + 1166092519364338103061624q^{27} + 2899576251477878827068378q^{29} + 15816960746665911900076128q^{31} + 51019828271446575126952080q^{33} + 104388880678377160773832848q^{35} + 34785435467211797617907442q^{37} + 135170503164419330229696168q^{39} - 673854719392272123121298562q^{41} - 1557799443962179540641188220q^{43} - 8295378544987729028249800086q^{45} - 7226966919683191159587179376q^{47} - 4755447639624414087245018709q^{49} + 24102421034763142313708267736q^{51} + 54068957931214078433925305634q^{53} + 72116739028709103312702411480q^{55} + 276172301449046303471104708848q^{57} + 201006239114458347216752503476q^{59} + 59158715139739534320593297466q^{61} - 1234485289426293666626080288968q^{63} - 2252651168064734881763466967812q^{65} - 2904325260543190867603068997428q^{67} - 1526403599797234628609099310816q^{69} + 1693346400885181878584585353944q^{71} + 1318409001451717739930563879902q^{73} + 20178451712790450065114527827828q^{75} + 20835723633799560796766684178720q^{77} + 43046757284148836281181573950704q^{79} + 60385181780035992188351168542827q^{81} - 71356083882380783036145089288964q^{83} - 137360972548514627995666767037884q^{85} - 253975679679758553189305216266392q^{87} - 194457621978564019473800095872498q^{89} - 384667165850137479369424211871408q^{91} + 554725843432039554369917205602688q^{93} - 205626706338774416034575296820376q^{95} + 566218664019390927229117474480422q^{97} + 2255131944887948953089434155026900q^{99} + O(q^{100}) \)

Decomposition of \(S_{34}^{\mathrm{new}}(\Gamma_1(4))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
4.34.a \(\chi_{4}(1, \cdot)\) 4.34.a.a 3 1

Decomposition of \(S_{34}^{\mathrm{old}}(\Gamma_1(4))\) into lower level spaces

\( S_{34}^{\mathrm{old}}(\Gamma_1(4)) \cong \) \(S_{34}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 - 92491788 T + 9599774056706745 T^{2} - \)\(84\!\cdots\!36\)\( T^{3} + \)\(53\!\cdots\!35\)\( T^{4} - \)\(28\!\cdots\!52\)\( T^{5} + \)\(17\!\cdots\!67\)\( T^{6} \)
$5$ \( 1 + 53880683886 T + \)\(46\!\cdots\!75\)\( T^{2} - \)\(45\!\cdots\!00\)\( T^{3} + \)\(54\!\cdots\!75\)\( T^{4} + \)\(73\!\cdots\!50\)\( T^{5} + \)\(15\!\cdots\!25\)\( T^{6} \)
$7$ \( 1 - 4541009914392 T + \)\(13\!\cdots\!97\)\( T^{2} - \)\(39\!\cdots\!80\)\( T^{3} + \)\(10\!\cdots\!79\)\( T^{4} - \)\(27\!\cdots\!08\)\( T^{5} + \)\(46\!\cdots\!43\)\( T^{6} \)
$11$ \( 1 - 227617657302449700 T + \)\(19\!\cdots\!93\)\( T^{2} + \)\(71\!\cdots\!00\)\( T^{3} + \)\(45\!\cdots\!83\)\( T^{4} - \)\(12\!\cdots\!00\)\( T^{5} + \)\(12\!\cdots\!91\)\( T^{6} \)
$13$ \( 1 - 272970442217358762 T + \)\(13\!\cdots\!95\)\( T^{2} - \)\(28\!\cdots\!04\)\( T^{3} + \)\(75\!\cdots\!35\)\( T^{4} - \)\(90\!\cdots\!58\)\( T^{5} + \)\(19\!\cdots\!77\)\( T^{6} \)
$17$ \( 1 - 93037188311816716854 T + \)\(10\!\cdots\!75\)\( T^{2} - \)\(76\!\cdots\!52\)\( T^{3} + \)\(41\!\cdots\!75\)\( T^{4} - \)\(15\!\cdots\!26\)\( T^{5} + \)\(65\!\cdots\!53\)\( T^{6} \)
$19$ \( 1 - \)\(13\!\cdots\!28\)\( T + \)\(39\!\cdots\!05\)\( T^{2} - \)\(35\!\cdots\!80\)\( T^{3} + \)\(61\!\cdots\!95\)\( T^{4} - \)\(33\!\cdots\!68\)\( T^{5} + \)\(39\!\cdots\!79\)\( T^{6} \)
$23$ \( 1 - \)\(11\!\cdots\!96\)\( T + \)\(18\!\cdots\!73\)\( T^{2} - \)\(14\!\cdots\!40\)\( T^{3} + \)\(16\!\cdots\!59\)\( T^{4} - \)\(87\!\cdots\!44\)\( T^{5} + \)\(64\!\cdots\!87\)\( T^{6} \)
$29$ \( 1 - \)\(28\!\cdots\!78\)\( T + \)\(43\!\cdots\!95\)\( T^{2} - \)\(47\!\cdots\!60\)\( T^{3} + \)\(79\!\cdots\!55\)\( T^{4} - \)\(95\!\cdots\!38\)\( T^{5} + \)\(59\!\cdots\!69\)\( T^{6} \)
$31$ \( 1 - \)\(15\!\cdots\!28\)\( T + \)\(13\!\cdots\!01\)\( T^{2} - \)\(66\!\cdots\!72\)\( T^{3} + \)\(21\!\cdots\!91\)\( T^{4} - \)\(42\!\cdots\!68\)\( T^{5} + \)\(44\!\cdots\!71\)\( T^{6} \)
$37$ \( 1 - \)\(34\!\cdots\!42\)\( T + \)\(58\!\cdots\!87\)\( T^{2} - \)\(50\!\cdots\!80\)\( T^{3} + \)\(32\!\cdots\!39\)\( T^{4} - \)\(11\!\cdots\!78\)\( T^{5} + \)\(17\!\cdots\!73\)\( T^{6} \)
$41$ \( 1 + \)\(67\!\cdots\!62\)\( T + \)\(59\!\cdots\!11\)\( T^{2} + \)\(21\!\cdots\!68\)\( T^{3} + \)\(98\!\cdots\!31\)\( T^{4} + \)\(18\!\cdots\!42\)\( T^{5} + \)\(46\!\cdots\!61\)\( T^{6} \)
$43$ \( 1 + \)\(15\!\cdots\!20\)\( T + \)\(22\!\cdots\!29\)\( T^{2} + \)\(19\!\cdots\!20\)\( T^{3} + \)\(18\!\cdots\!47\)\( T^{4} + \)\(10\!\cdots\!80\)\( T^{5} + \)\(51\!\cdots\!07\)\( T^{6} \)
$47$ \( 1 + \)\(72\!\cdots\!76\)\( T + \)\(60\!\cdots\!05\)\( T^{2} + \)\(22\!\cdots\!28\)\( T^{3} + \)\(91\!\cdots\!35\)\( T^{4} + \)\(16\!\cdots\!04\)\( T^{5} + \)\(34\!\cdots\!83\)\( T^{6} \)
$53$ \( 1 - \)\(54\!\cdots\!34\)\( T + \)\(28\!\cdots\!83\)\( T^{2} - \)\(80\!\cdots\!40\)\( T^{3} + \)\(23\!\cdots\!59\)\( T^{4} - \)\(34\!\cdots\!86\)\( T^{5} + \)\(50\!\cdots\!17\)\( T^{6} \)
$59$ \( 1 - \)\(20\!\cdots\!76\)\( T + \)\(56\!\cdots\!29\)\( T^{2} - \)\(65\!\cdots\!96\)\( T^{3} + \)\(15\!\cdots\!91\)\( T^{4} - \)\(15\!\cdots\!16\)\( T^{5} + \)\(20\!\cdots\!39\)\( T^{6} \)
$61$ \( 1 - \)\(59\!\cdots\!66\)\( T + \)\(26\!\cdots\!95\)\( T^{2} - \)\(28\!\cdots\!40\)\( T^{3} + \)\(21\!\cdots\!95\)\( T^{4} - \)\(40\!\cdots\!26\)\( T^{5} + \)\(55\!\cdots\!41\)\( T^{6} \)
$67$ \( 1 + \)\(29\!\cdots\!28\)\( T + \)\(81\!\cdots\!37\)\( T^{2} + \)\(11\!\cdots\!00\)\( T^{3} + \)\(14\!\cdots\!19\)\( T^{4} + \)\(96\!\cdots\!32\)\( T^{5} + \)\(60\!\cdots\!03\)\( T^{6} \)
$71$ \( 1 - \)\(16\!\cdots\!44\)\( T + \)\(30\!\cdots\!45\)\( T^{2} - \)\(32\!\cdots\!60\)\( T^{3} + \)\(37\!\cdots\!95\)\( T^{4} - \)\(25\!\cdots\!24\)\( T^{5} + \)\(18\!\cdots\!31\)\( T^{6} \)
$73$ \( 1 - \)\(13\!\cdots\!02\)\( T + \)\(36\!\cdots\!75\)\( T^{2} - \)\(19\!\cdots\!84\)\( T^{3} + \)\(11\!\cdots\!75\)\( T^{4} - \)\(12\!\cdots\!78\)\( T^{5} + \)\(29\!\cdots\!37\)\( T^{6} \)
$79$ \( 1 - \)\(43\!\cdots\!04\)\( T + \)\(15\!\cdots\!89\)\( T^{2} - \)\(35\!\cdots\!44\)\( T^{3} + \)\(62\!\cdots\!71\)\( T^{4} - \)\(75\!\cdots\!84\)\( T^{5} + \)\(73\!\cdots\!19\)\( T^{6} \)
$83$ \( 1 + \)\(71\!\cdots\!64\)\( T + \)\(66\!\cdots\!93\)\( T^{2} + \)\(26\!\cdots\!20\)\( T^{3} + \)\(14\!\cdots\!59\)\( T^{4} + \)\(32\!\cdots\!16\)\( T^{5} + \)\(97\!\cdots\!47\)\( T^{6} \)
$89$ \( 1 + \)\(19\!\cdots\!98\)\( T + \)\(63\!\cdots\!75\)\( T^{2} + \)\(76\!\cdots\!20\)\( T^{3} + \)\(13\!\cdots\!75\)\( T^{4} + \)\(88\!\cdots\!78\)\( T^{5} + \)\(97\!\cdots\!09\)\( T^{6} \)
$97$ \( 1 - \)\(56\!\cdots\!22\)\( T - \)\(50\!\cdots\!73\)\( T^{2} + \)\(35\!\cdots\!00\)\( T^{3} - \)\(18\!\cdots\!21\)\( T^{4} - \)\(75\!\cdots\!38\)\( T^{5} + \)\(49\!\cdots\!33\)\( T^{6} \)
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