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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

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

Display 100 coefficients 10 coefficients

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 available 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

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