Properties

Label 18.8.a
Level 18
Weight 8
Character orbit a
Rep. character \(\chi_{18}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 2
Sturm bound 24
Trace bound 2

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Defining parameters

Level: \( N \) = \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 18.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(18))\).

Total New Old
Modular forms 25 2 23
Cusp forms 17 2 15
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.
\(+\)\(-\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(1\)

Trace form

\(2q \) \(\mathstrut +\mathstrut 128q^{4} \) \(\mathstrut +\mathstrut 324q^{5} \) \(\mathstrut -\mathstrut 560q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 128q^{4} \) \(\mathstrut +\mathstrut 324q^{5} \) \(\mathstrut -\mathstrut 560q^{7} \) \(\mathstrut +\mathstrut 768q^{10} \) \(\mathstrut -\mathstrut 8424q^{11} \) \(\mathstrut -\mathstrut 2420q^{13} \) \(\mathstrut +\mathstrut 20736q^{14} \) \(\mathstrut +\mathstrut 8192q^{16} \) \(\mathstrut -\mathstrut 8100q^{17} \) \(\mathstrut -\mathstrut 15080q^{19} \) \(\mathstrut +\mathstrut 20736q^{20} \) \(\mathstrut +\mathstrut 49920q^{22} \) \(\mathstrut -\mathstrut 110160q^{23} \) \(\mathstrut -\mathstrut 99154q^{25} \) \(\mathstrut +\mathstrut 41472q^{26} \) \(\mathstrut -\mathstrut 35840q^{28} \) \(\mathstrut +\mathstrut 144180q^{29} \) \(\mathstrut +\mathstrut 260704q^{31} \) \(\mathstrut -\mathstrut 170496q^{34} \) \(\mathstrut +\mathstrut 33696q^{35} \) \(\mathstrut +\mathstrut 124060q^{37} \) \(\mathstrut -\mathstrut 518400q^{38} \) \(\mathstrut +\mathstrut 49152q^{40} \) \(\mathstrut +\mathstrut 628236q^{41} \) \(\mathstrut -\mathstrut 787160q^{43} \) \(\mathstrut -\mathstrut 539136q^{44} \) \(\mathstrut -\mathstrut 218112q^{46} \) \(\mathstrut -\mathstrut 38880q^{47} \) \(\mathstrut +\mathstrut 1868946q^{49} \) \(\mathstrut +\mathstrut 248832q^{50} \) \(\mathstrut -\mathstrut 154880q^{52} \) \(\mathstrut +\mathstrut 707940q^{53} \) \(\mathstrut -\mathstrut 1065168q^{55} \) \(\mathstrut +\mathstrut 1327104q^{56} \) \(\mathstrut +\mathstrut 487680q^{58} \) \(\mathstrut -\mathstrut 3385800q^{59} \) \(\mathstrut -\mathstrut 832916q^{61} \) \(\mathstrut +\mathstrut 1555200q^{62} \) \(\mathstrut +\mathstrut 524288q^{64} \) \(\mathstrut -\mathstrut 143208q^{65} \) \(\mathstrut -\mathstrut 3416840q^{67} \) \(\mathstrut -\mathstrut 518400q^{68} \) \(\mathstrut +\mathstrut 3144192q^{70} \) \(\mathstrut -\mathstrut 4301424q^{71} \) \(\mathstrut +\mathstrut 3640180q^{73} \) \(\mathstrut +\mathstrut 1575936q^{74} \) \(\mathstrut -\mathstrut 965120q^{76} \) \(\mathstrut +\mathstrut 10445760q^{77} \) \(\mathstrut +\mathstrut 240640q^{79} \) \(\mathstrut +\mathstrut 1327104q^{80} \) \(\mathstrut -\mathstrut 5199360q^{82} \) \(\mathstrut -\mathstrut 7902360q^{83} \) \(\mathstrut -\mathstrut 2335176q^{85} \) \(\mathstrut -\mathstrut 3794688q^{86} \) \(\mathstrut +\mathstrut 3194880q^{88} \) \(\mathstrut +\mathstrut 5959980q^{89} \) \(\mathstrut +\mathstrut 7396064q^{91} \) \(\mathstrut -\mathstrut 7050240q^{92} \) \(\mathstrut -\mathstrut 7251456q^{94} \) \(\mathstrut -\mathstrut 5553360q^{95} \) \(\mathstrut +\mathstrut 4622020q^{97} \) \(\mathstrut -\mathstrut 11612160q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(18))\) 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
18.8.a.a \(1\) \(5.623\) \(\Q\) None \(-8\) \(0\) \(114\) \(-1576\) \(+\) \(-\) \(q-8q^{2}+2^{6}q^{4}+114q^{5}-1576q^{7}+\cdots\)
18.8.a.b \(1\) \(5.623\) \(\Q\) None \(8\) \(0\) \(210\) \(1016\) \(-\) \(-\) \(q+8q^{2}+2^{6}q^{4}+210q^{5}+1016q^{7}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(18))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(18)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)