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Properties

Label 4.36.a
Level $4$
Weight $36$
Character orbit 4.a
Rep. character $\chi_{4}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $1$
Sturm bound $18$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 4 = 2^{2} \)
Weight: \( k \) \(=\) \( 36 \)
Character orbit: \([\chi]\) \(=\) 4.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{36}(\Gamma_0(4))\).

Total New Old
Modular forms 19 3 16
Cusp forms 16 3 13
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

\( 3 q + 50908884 q^{3} + 280720890 q^{5} - 5549296289016 q^{7} - 4115694118097313 q^{9} + O(q^{10}) \) \( 3 q + 50908884 q^{3} + 280720890 q^{5} - 5549296289016 q^{7} - 4115694118097313 q^{9} - 420463958869151460 q^{11} - 7370701315414736574 q^{13} + 35737802623493622360 q^{15} + 616802274448822103958 q^{17} - 3523177807465210008348 q^{19} - 35614415089970552016672 q^{21} - 97200569155131383968872 q^{23} - 1397444430311587979767275 q^{25} - 13813263585892101497770872 q^{27} - 72104888547394509330484398 q^{29} - 305306760334252700869662432 q^{31} - 1206118755141042924734246640 q^{33} - 4139993873456897291989313040 q^{35} - 10467805589252853184477978086 q^{37} - 21306312046147482048067771848 q^{39} - 28614809221544804827249675602 q^{41} - 20661331953141752160177135300 q^{43} + 109445534106618058172074201410 q^{45} + 431671100729347757519313060528 q^{47} + 1202271820749265164710734860219 q^{49} + 1812312130969213433267629787496 q^{51} + 2094590682902326557681205190442 q^{53} - 424018895462656971242660883000 q^{55} - 7056738639317962169249569687824 q^{57} - 21898322952557962385462881418676 q^{59} - 46553596324122391351852871731854 q^{61} - 60534256794589553738854966512984 q^{63} - 47301026213190020793582172528260 q^{65} + 75982094975394264303461043768084 q^{67} + 266168516453886472772566159456416 q^{69} + 591751031973420639599491172643144 q^{71} + 840249720714294658198657086588366 q^{73} + 844328642366224046122007927037900 q^{75} + 366867399909875520359123617491360 q^{77} - 1512021839065233136089826558058544 q^{79} - 4715323858342810015899488694567333 q^{81} - 8944825848970974146478286242709212 q^{83} - 11518175153366806194794571426747180 q^{85} - 9434346897547249340232797055364104 q^{87} + 1625382197094823895014829864559198 q^{89} + 28933989451866564710063788057094832 q^{91} + 43351982414907351295090224432607104 q^{93} + 96155354088435090124008638354927160 q^{95} + 83007021412015685382745763811847014 q^{97} + 91112511762343802272300511308928460 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{36}^{\mathrm{new}}(\Gamma_0(4))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2
4.36.a.a 4.a 1.a $3$ $31.038$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(50908884\) \(280720890\) \(-55\!\cdots\!16\) $-$ $\mathrm{SU}(2)$ \(q+(16969628+\beta _{1})q^{3}+(93573630+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{36}^{\mathrm{old}}(\Gamma_0(4))\) into lower level spaces

\( S_{36}^{\mathrm{old}}(\Gamma_0(4)) \cong \) \(S_{36}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{36}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)