Properties

Label 18.4.a
Level 18
Weight 4
Character orbit a
Rep. character \(\chi_{18}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) = \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 18.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 13 1 12
Cusp forms 5 1 4
Eisenstein series 8 0 8

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)FrickeDim.
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(0\)

Trace form

\(q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 16q^{7} \) \(\mathstrut +\mathstrut 8q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 16q^{7} \) \(\mathstrut +\mathstrut 8q^{8} \) \(\mathstrut -\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut +\mathstrut 38q^{13} \) \(\mathstrut -\mathstrut 32q^{14} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut +\mathstrut 126q^{17} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 24q^{20} \) \(\mathstrut -\mathstrut 24q^{22} \) \(\mathstrut -\mathstrut 168q^{23} \) \(\mathstrut -\mathstrut 89q^{25} \) \(\mathstrut +\mathstrut 76q^{26} \) \(\mathstrut -\mathstrut 64q^{28} \) \(\mathstrut -\mathstrut 30q^{29} \) \(\mathstrut -\mathstrut 88q^{31} \) \(\mathstrut +\mathstrut 32q^{32} \) \(\mathstrut +\mathstrut 252q^{34} \) \(\mathstrut +\mathstrut 96q^{35} \) \(\mathstrut +\mathstrut 254q^{37} \) \(\mathstrut +\mathstrut 40q^{38} \) \(\mathstrut -\mathstrut 48q^{40} \) \(\mathstrut -\mathstrut 42q^{41} \) \(\mathstrut -\mathstrut 52q^{43} \) \(\mathstrut -\mathstrut 48q^{44} \) \(\mathstrut -\mathstrut 336q^{46} \) \(\mathstrut +\mathstrut 96q^{47} \) \(\mathstrut -\mathstrut 87q^{49} \) \(\mathstrut -\mathstrut 178q^{50} \) \(\mathstrut +\mathstrut 152q^{52} \) \(\mathstrut -\mathstrut 198q^{53} \) \(\mathstrut +\mathstrut 72q^{55} \) \(\mathstrut -\mathstrut 128q^{56} \) \(\mathstrut -\mathstrut 60q^{58} \) \(\mathstrut +\mathstrut 660q^{59} \) \(\mathstrut -\mathstrut 538q^{61} \) \(\mathstrut -\mathstrut 176q^{62} \) \(\mathstrut +\mathstrut 64q^{64} \) \(\mathstrut -\mathstrut 228q^{65} \) \(\mathstrut +\mathstrut 884q^{67} \) \(\mathstrut +\mathstrut 504q^{68} \) \(\mathstrut +\mathstrut 192q^{70} \) \(\mathstrut -\mathstrut 792q^{71} \) \(\mathstrut +\mathstrut 218q^{73} \) \(\mathstrut +\mathstrut 508q^{74} \) \(\mathstrut +\mathstrut 80q^{76} \) \(\mathstrut +\mathstrut 192q^{77} \) \(\mathstrut -\mathstrut 520q^{79} \) \(\mathstrut -\mathstrut 96q^{80} \) \(\mathstrut -\mathstrut 84q^{82} \) \(\mathstrut +\mathstrut 492q^{83} \) \(\mathstrut -\mathstrut 756q^{85} \) \(\mathstrut -\mathstrut 104q^{86} \) \(\mathstrut -\mathstrut 96q^{88} \) \(\mathstrut -\mathstrut 810q^{89} \) \(\mathstrut -\mathstrut 608q^{91} \) \(\mathstrut -\mathstrut 672q^{92} \) \(\mathstrut +\mathstrut 192q^{94} \) \(\mathstrut -\mathstrut 120q^{95} \) \(\mathstrut +\mathstrut 1154q^{97} \) \(\mathstrut -\mathstrut 174q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
18.4.a.a \(1\) \(1.062\) \(\Q\) None \(2\) \(0\) \(-6\) \(-16\) \(-\) \(-\) \(q+2q^{2}+4q^{4}-6q^{5}-2^{4}q^{7}+8q^{8}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(\Gamma_0(18)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)