Properties

Label 4.24.a
Level 4
Weight 24
Character orbit a
Rep. character \(\chi_{4}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 12
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 24 \)
Character orbit: \([\chi]\) = 4.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_0(4))\).

Total New Old
Modular forms 13 2 11
Cusp forms 10 2 8
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.
\(-\)\(2\)

Trace form

\( 2q + 170520q^{3} - 92266020q^{5} + 192083440q^{7} + 8599879818q^{9} + O(q^{10}) \) \( 2q + 170520q^{3} - 92266020q^{5} + 192083440q^{7} + 8599879818q^{9} - 1247174695800q^{11} - 7460299980980q^{13} - 106334360092080q^{15} - 374897347903260q^{17} - 840360279212552q^{19} + 400401295079232q^{21} + 6433357923072720q^{23} + 33587241295679150q^{25} + 15773861091124080q^{27} - 68055499247434452q^{29} - 145584514546845248q^{31} - 650343867352613280q^{33} - 216234488190163680q^{35} + 1211894143551157660q^{37} + 3553993994899379088q^{39} + 5036778367134688692q^{41} + 935180945919935560q^{43} - 17187460645010169780q^{45} - 8431168896277596000q^{47} - 53910291562566659694q^{49} - 4938798717170442576q^{51} + 3763137197370204540q^{53} + 351301189218989209200q^{55} - 43703893486254219360q^{57} + 348561606512901387816q^{59} - 582966592720711355156q^{61} + 66309764232647559600q^{63} - 1918465858864426149720q^{65} + 211615268845414654360q^{67} - 1499363181860662472256q^{69} + 3840047757133544010096q^{71} - 680666251913594096780q^{73} + 11948876435052098946600q^{75} - 1265465342298122095680q^{77} - 642991395306723640736q^{79} - 13196380320218478599982q^{81} - 18799502632508717771400q^{83} + 2701670550661359899640q^{85} - 26089604267151850210800q^{87} + 5001398778883250139732q^{89} + 8107764572821621082528q^{91} + 104099589081258166744320q^{93} + 23677928248035152895120q^{95} + 122022794260559820614980q^{97} - 98127319293495379027800q^{99} + O(q^{100}) \)

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_0(4))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
4.24.a.a \(2\) \(13.408\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(0\) \(170520\) \(-92266020\) \(192083440\) \(-\) \(q+(85260-\beta )q^{3}+(-46133010+540\beta )q^{5}+\cdots\)

Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_0(4))\) into lower level spaces

\( S_{24}^{\mathrm{old}}(\Gamma_0(4)) \cong \) \(S_{24}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)