Properties

Label 4.10.a
Level $4$
Weight $10$
Character orbit 4.a
Rep. character $\chi_{4}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $5$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 4 = 2^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 4.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(4))\).

Total New Old
Modular forms 6 1 5
Cusp forms 3 1 2
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
\(-\)\(1\)

Trace form

\( q + 228 q^{3} - 666 q^{5} - 6328 q^{7} + 32301 q^{9} + O(q^{10}) \) \( q + 228 q^{3} - 666 q^{5} - 6328 q^{7} + 32301 q^{9} - 30420 q^{11} - 32338 q^{13} - 151848 q^{15} + 590994 q^{17} + 34676 q^{19} - 1442784 q^{21} + 1048536 q^{23} - 1509569 q^{25} + 2876904 q^{27} + 4409406 q^{29} - 7401184 q^{31} - 6935760 q^{33} + 4214448 q^{35} + 10234502 q^{37} - 7373064 q^{39} + 18352746 q^{41} - 252340 q^{43} - 21512466 q^{45} - 49517136 q^{47} - 310023 q^{49} + 134746632 q^{51} - 66396906 q^{53} + 20259720 q^{55} + 7906128 q^{57} - 61523748 q^{59} + 35638622 q^{61} - 204400728 q^{63} + 21537108 q^{65} + 181742372 q^{67} + 239066208 q^{69} + 90904968 q^{71} - 262978678 q^{73} - 344181732 q^{75} + 192497760 q^{77} - 116502832 q^{79} + 20153529 q^{81} - 9563724 q^{83} - 393602004 q^{85} + 1005344568 q^{87} + 611826714 q^{89} + 204634864 q^{91} - 1687469952 q^{93} - 23094216 q^{95} - 259312798 q^{97} - 982596420 q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(4))\) 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
4.10.a.a 4.a 1.a $1$ $2.060$ \(\Q\) None \(0\) \(228\) \(-666\) \(-6328\) $-$ $\mathrm{SU}(2)$ \(q+228q^{3}-666q^{5}-6328q^{7}+32301q^{9}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(4))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(4)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)