Properties

Label 4.34.a
Level 4
Weight 34
Character orbit a
Rep. character \(\chi_{4}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newform subspaces 1
Sturm bound 17
Trace bound 0

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Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 34 \)
Character orbit: \([\chi]\) = 4.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(17\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{34}(\Gamma_0(4))\).

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

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

\(2\)Dim.
\(-\)\(3\)

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 \(S_{34}^{\mathrm{new}}(\Gamma_0(4))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
4.34.a.a \(3\) \(27.593\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(92491788\) \(-53880683886\) \(45\!\cdots\!92\) \(-\) \(q+(30830596+\beta _{1})q^{3}+(-17960227962+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{34}^{\mathrm{old}}(\Gamma_0(4))\) into lower level spaces

\( S_{34}^{\mathrm{old}}(\Gamma_0(4)) \cong \) \(S_{34}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)