Properties

Label 4.10.a
Level 4
Weight 10
Character orbit a
Rep. character \(\chi_{4}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 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: \(\Q\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(4))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
4.10.a.a \(1\) \(2.060\) \(\Q\) None \(0\) \(228\) \(-666\) \(-6328\) \(-\) \(q+228q^{3}-666q^{5}-6328q^{7}+32301q^{9}+\cdots\)

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

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