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Properties

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

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Defining parameters

Level: \( N \) \(=\) \( 4 = 2^{2} \)
Weight: \( k \) \(=\) \( 24 \)
Character orbit: \([\chi]\) \(=\) 4.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_0(4))\) 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
4.24.a.a 4.a 1.a $2$ $13.408$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(0\) \(170520\) \(-92266020\) \(192083440\) $-$ $\mathrm{SU}(2)$ \(q+(85260-\beta )q^{3}+(-46133010+540\beta )q^{5}+\cdots\)

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

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