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

Related objects

Downloads

Learn more about

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

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

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

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