Properties

Label 4.22.a
Level 4
Weight 22
Character orbit a
Rep. character \(\chi_{4}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 11
Trace bound 0

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Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 22 \)
Character orbit: \([\chi]\) = 4.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(11\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_0(4))\).

Total New Old
Modular forms 12 2 10
Cusp forms 9 2 7
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

\(2q \) \(\mathstrut +\mathstrut 65640q^{3} \) \(\mathstrut +\mathstrut 13689324q^{5} \) \(\mathstrut -\mathstrut 260508080q^{7} \) \(\mathstrut +\mathstrut 12461535162q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 65640q^{3} \) \(\mathstrut +\mathstrut 13689324q^{5} \) \(\mathstrut -\mathstrut 260508080q^{7} \) \(\mathstrut +\mathstrut 12461535162q^{9} \) \(\mathstrut +\mathstrut 145435963320q^{11} \) \(\mathstrut +\mathstrut 1428900417340q^{13} \) \(\mathstrut +\mathstrut 6819782714352q^{15} \) \(\mathstrut +\mathstrut 1840620576420q^{17} \) \(\mathstrut -\mathstrut 16780743928568q^{19} \) \(\mathstrut -\mathstrut 192357511002048q^{21} \) \(\mathstrut -\mathstrut 319691925426960q^{23} \) \(\mathstrut +\mathstrut 439606295919326q^{25} \) \(\mathstrut +\mathstrut 1772171769223440q^{27} \) \(\mathstrut +\mathstrut 3742111775766492q^{29} \) \(\mathstrut +\mathstrut 112042353462592q^{31} \) \(\mathstrut -\mathstrut 5046260260851360q^{33} \) \(\mathstrut -\mathstrut 39279847462424352q^{35} \) \(\mathstrut -\mathstrut 33362705637547220q^{37} \) \(\mathstrut +\mathstrut 36755051864070192q^{39} \) \(\mathstrut +\mathstrut 175129744323133332q^{41} \) \(\mathstrut +\mathstrut 15346613416528120q^{43} \) \(\mathstrut +\mathstrut 503454557153115324q^{45} \) \(\mathstrut -\mathstrut 684848819288455200q^{47} \) \(\mathstrut -\mathstrut 1267753878311886q^{49} \) \(\mathstrut -\mathstrut 2589533339352286896q^{51} \) \(\mathstrut +\mathstrut 675305394244421580q^{53} \) \(\mathstrut -\mathstrut 1007711578141009200q^{55} \) \(\mathstrut +\mathstrut 7738689471355209120q^{57} \) \(\mathstrut +\mathstrut 1042445250435434904q^{59} \) \(\mathstrut +\mathstrut 9065997829736468764q^{61} \) \(\mathstrut -\mathstrut 13688298514444201200q^{63} \) \(\mathstrut +\mathstrut 7711482582413403048q^{65} \) \(\mathstrut -\mathstrut 30464301046802775320q^{67} \) \(\mathstrut -\mathstrut 30093532090729291584q^{69} \) \(\mathstrut -\mathstrut 8199093502830518064q^{71} \) \(\mathstrut +\mathstrut 25415086659374793940q^{73} \) \(\mathstrut +\mathstrut 101635704862879905048q^{75} \) \(\mathstrut +\mathstrut 38853770260581178560q^{77} \) \(\mathstrut +\mathstrut 121204353225060164896q^{79} \) \(\mathstrut -\mathstrut 136996120065469586382q^{81} \) \(\mathstrut +\mathstrut 108742936757033809800q^{83} \) \(\mathstrut -\mathstrut 527989845644919754344q^{85} \) \(\mathstrut -\mathstrut 24695689277789874000q^{87} \) \(\mathstrut -\mathstrut 184207999274965368972q^{89} \) \(\mathstrut -\mathstrut 126427419539014666912q^{91} \) \(\mathstrut -\mathstrut 139841964206001442560q^{93} \) \(\mathstrut +\mathstrut 1576185911066925315504q^{95} \) \(\mathstrut +\mathstrut 739497785188476467140q^{97} \) \(\mathstrut +\mathstrut 261627767970577922520q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_0(4))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
4.22.a.a \(2\) \(11.179\) \(\Q(\sqrt{2161}) \) None \(0\) \(65640\) \(13689324\) \(-260508080\) \(-\) \(q+(32820-\beta )q^{3}+(6844662-204\beta )q^{5}+\cdots\)

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_0(4))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_0(4)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)