Properties

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

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Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 34 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
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

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

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

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