Properties

Label 4.18.a
Level 4
Weight 18
Character orbit a
Rep. character \(\chi_{4}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 9
Trace bound 0

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Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 18 \)
Character orbit: \([\chi]\) = 4.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_0(4))\).

Total New Old
Modular forms 10 2 8
Cusp forms 7 2 5
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

\(2q \) \(\mathstrut -\mathstrut 5880q^{3} \) \(\mathstrut +\mathstrut 604044q^{5} \) \(\mathstrut +\mathstrut 25350160q^{7} \) \(\mathstrut +\mathstrut 449174682q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 5880q^{3} \) \(\mathstrut +\mathstrut 604044q^{5} \) \(\mathstrut +\mathstrut 25350160q^{7} \) \(\mathstrut +\mathstrut 449174682q^{9} \) \(\mathstrut +\mathstrut 1259648280q^{11} \) \(\mathstrut -\mathstrut 1320052580q^{13} \) \(\mathstrut -\mathstrut 26621930448q^{15} \) \(\mathstrut -\mathstrut 27498226140q^{17} \) \(\mathstrut +\mathstrut 101133633832q^{19} \) \(\mathstrut +\mathstrut 335430207552q^{21} \) \(\mathstrut +\mathstrut 134767491120q^{23} \) \(\mathstrut -\mathstrut 448986850114q^{25} \) \(\mathstrut -\mathstrut 4619416117680q^{27} \) \(\mathstrut +\mathstrut 2337155582652q^{29} \) \(\mathstrut +\mathstrut 278836113472q^{31} \) \(\mathstrut +\mathstrut 22602380058720q^{33} \) \(\mathstrut -\mathstrut 7102242382752q^{35} \) \(\mathstrut +\mathstrut 20929802888140q^{37} \) \(\mathstrut -\mathstrut 108447997173648q^{39} \) \(\mathstrut +\mathstrut 4166592315732q^{41} \) \(\mathstrut -\mathstrut 111143148534440q^{43} \) \(\mathstrut +\mathstrut 281755357404444q^{45} \) \(\mathstrut +\mathstrut 196772651157600q^{47} \) \(\mathstrut +\mathstrut 99570326741874q^{49} \) \(\mathstrut -\mathstrut 39956666918256q^{51} \) \(\mathstrut -\mathstrut 487965122736660q^{53} \) \(\mathstrut -\mathstrut 566565363246960q^{55} \) \(\mathstrut -\mathstrut 2272313631999840q^{57} \) \(\mathstrut +\mathstrut 2835904197813624q^{59} \) \(\mathstrut -\mathstrut 67544034994436q^{61} \) \(\mathstrut +\mathstrut 3282762121966800q^{63} \) \(\mathstrut +\mathstrut 3645157343001768q^{65} \) \(\mathstrut -\mathstrut 995171321546360q^{67} \) \(\mathstrut -\mathstrut 10188302100105024q^{69} \) \(\mathstrut +\mathstrut 3882245493215376q^{71} \) \(\mathstrut -\mathstrut 12746425881769580q^{73} \) \(\mathstrut -\mathstrut 13688080703624712q^{75} \) \(\mathstrut +\mathstrut 31591755846002880q^{77} \) \(\mathstrut -\mathstrut 14984271534065504q^{79} \) \(\mathstrut +\mathstrut 33380230287529458q^{81} \) \(\mathstrut +\mathstrut 43899417809893800q^{83} \) \(\mathstrut -\mathstrut 3956216991540264q^{85} \) \(\mathstrut -\mathstrut 100892756486768400q^{87} \) \(\mathstrut +\mathstrut 51909007958846388q^{89} \) \(\mathstrut -\mathstrut 83455169400462112q^{91} \) \(\mathstrut -\mathstrut 89807116632334080q^{93} \) \(\mathstrut +\mathstrut 101643889304423664q^{95} \) \(\mathstrut -\mathstrut 49281007789848380q^{97} \) \(\mathstrut +\mathstrut 128223271309133880q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_0(4))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
4.18.a.a \(2\) \(7.329\) \(\Q(\sqrt{9361}) \) None \(0\) \(-5880\) \(604044\) \(25350160\) \(-\) \(q+(-2940-\beta )q^{3}+(302022+6^{2}\beta )q^{5}+\cdots\)

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_0(4))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_0(4)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)