Properties

Label 18.6.a
Level 18
Weight 6
Character orbit a
Rep. character \(\chi_{18}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 3
Sturm bound 18
Trace bound 5

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Defining parameters

Level: \( N \) = \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 18.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(18\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(18))\).

Total New Old
Modular forms 19 3 16
Cusp forms 11 3 8
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.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(2\)

Trace form

\(3q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 48q^{4} \) \(\mathstrut +\mathstrut 66q^{5} \) \(\mathstrut -\mathstrut 120q^{7} \) \(\mathstrut -\mathstrut 64q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 48q^{4} \) \(\mathstrut +\mathstrut 66q^{5} \) \(\mathstrut -\mathstrut 120q^{7} \) \(\mathstrut -\mathstrut 64q^{8} \) \(\mathstrut +\mathstrut 504q^{10} \) \(\mathstrut +\mathstrut 60q^{11} \) \(\mathstrut -\mathstrut 1326q^{13} \) \(\mathstrut -\mathstrut 704q^{14} \) \(\mathstrut +\mathstrut 768q^{16} \) \(\mathstrut +\mathstrut 414q^{17} \) \(\mathstrut -\mathstrut 372q^{19} \) \(\mathstrut +\mathstrut 1056q^{20} \) \(\mathstrut -\mathstrut 3312q^{22} \) \(\mathstrut -\mathstrut 600q^{23} \) \(\mathstrut +\mathstrut 13413q^{25} \) \(\mathstrut +\mathstrut 2632q^{26} \) \(\mathstrut -\mathstrut 1920q^{28} \) \(\mathstrut -\mathstrut 5574q^{29} \) \(\mathstrut -\mathstrut 12720q^{31} \) \(\mathstrut -\mathstrut 1024q^{32} \) \(\mathstrut -\mathstrut 6264q^{34} \) \(\mathstrut +\mathstrut 11616q^{35} \) \(\mathstrut +\mathstrut 3138q^{37} \) \(\mathstrut -\mathstrut 3824q^{38} \) \(\mathstrut +\mathstrut 8064q^{40} \) \(\mathstrut -\mathstrut 19194q^{41} \) \(\mathstrut -\mathstrut 16428q^{43} \) \(\mathstrut +\mathstrut 960q^{44} \) \(\mathstrut +\mathstrut 33120q^{46} \) \(\mathstrut +\mathstrut 19680q^{47} \) \(\mathstrut +\mathstrut 24363q^{49} \) \(\mathstrut -\mathstrut 4924q^{50} \) \(\mathstrut -\mathstrut 21216q^{52} \) \(\mathstrut +\mathstrut 31266q^{53} \) \(\mathstrut -\mathstrut 69768q^{55} \) \(\mathstrut -\mathstrut 11264q^{56} \) \(\mathstrut +\mathstrut 21528q^{58} \) \(\mathstrut -\mathstrut 26340q^{59} \) \(\mathstrut +\mathstrut 54474q^{61} \) \(\mathstrut +\mathstrut 14368q^{62} \) \(\mathstrut +\mathstrut 12288q^{64} \) \(\mathstrut -\mathstrut 43428q^{65} \) \(\mathstrut +\mathstrut 56508q^{67} \) \(\mathstrut +\mathstrut 6624q^{68} \) \(\mathstrut -\mathstrut 160128q^{70} \) \(\mathstrut -\mathstrut 6120q^{71} \) \(\mathstrut -\mathstrut 59178q^{73} \) \(\mathstrut +\mathstrut 33832q^{74} \) \(\mathstrut -\mathstrut 5952q^{76} \) \(\mathstrut +\mathstrut 10560q^{77} \) \(\mathstrut +\mathstrut 130560q^{79} \) \(\mathstrut +\mathstrut 16896q^{80} \) \(\mathstrut +\mathstrut 130536q^{82} \) \(\mathstrut +\mathstrut 6468q^{83} \) \(\mathstrut -\mathstrut 83268q^{85} \) \(\mathstrut -\mathstrut 53264q^{86} \) \(\mathstrut -\mathstrut 52992q^{88} \) \(\mathstrut +\mathstrut 32742q^{89} \) \(\mathstrut -\mathstrut 16944q^{91} \) \(\mathstrut -\mathstrut 9600q^{92} \) \(\mathstrut +\mathstrut 74880q^{94} \) \(\mathstrut +\mathstrut 63096q^{95} \) \(\mathstrut +\mathstrut 106206q^{97} \) \(\mathstrut -\mathstrut 56676q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(18))\) 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
18.6.a.a \(1\) \(2.887\) \(\Q\) None \(-4\) \(0\) \(-96\) \(-148\) \(+\) \(+\) \(q-4q^{2}+2^{4}q^{4}-96q^{5}-148q^{7}+\cdots\)
18.6.a.b \(1\) \(2.887\) \(\Q\) None \(-4\) \(0\) \(66\) \(176\) \(+\) \(-\) \(q-4q^{2}+2^{4}q^{4}+66q^{5}+176q^{7}+\cdots\)
18.6.a.c \(1\) \(2.887\) \(\Q\) None \(4\) \(0\) \(96\) \(-148\) \(-\) \(+\) \(q+4q^{2}+2^{4}q^{4}+96q^{5}-148q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(18))\) into lower level spaces

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