Properties

Label 18.12.a
Level 18
Weight 12
Character orbit a
Rep. character \(\chi_{18}(1,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 5
Sturm bound 36
Trace bound 5

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Defining parameters

Level: \( N \) = \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 18.a (trivial)
Character field: \(\Q\)
Newforms: \( 5 \)
Sturm bound: \(36\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(18))\).

Total New Old
Modular forms 37 5 32
Cusp forms 29 5 24
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.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(3\)
Minus space\(-\)\(2\)

Trace form

\(5q \) \(\mathstrut +\mathstrut 32q^{2} \) \(\mathstrut +\mathstrut 5120q^{4} \) \(\mathstrut +\mathstrut 2334q^{5} \) \(\mathstrut -\mathstrut 42680q^{7} \) \(\mathstrut +\mathstrut 32768q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut +\mathstrut 32q^{2} \) \(\mathstrut +\mathstrut 5120q^{4} \) \(\mathstrut +\mathstrut 2334q^{5} \) \(\mathstrut -\mathstrut 42680q^{7} \) \(\mathstrut +\mathstrut 32768q^{8} \) \(\mathstrut -\mathstrut 30912q^{10} \) \(\mathstrut +\mathstrut 1699116q^{11} \) \(\mathstrut -\mathstrut 828698q^{13} \) \(\mathstrut -\mathstrut 335360q^{14} \) \(\mathstrut +\mathstrut 5242880q^{16} \) \(\mathstrut -\mathstrut 8603622q^{17} \) \(\mathstrut +\mathstrut 33308092q^{19} \) \(\mathstrut +\mathstrut 2390016q^{20} \) \(\mathstrut -\mathstrut 20705664q^{22} \) \(\mathstrut +\mathstrut 1057800q^{23} \) \(\mathstrut -\mathstrut 4367269q^{25} \) \(\mathstrut +\mathstrut 165855424q^{26} \) \(\mathstrut -\mathstrut 43704320q^{28} \) \(\mathstrut -\mathstrut 70389066q^{29} \) \(\mathstrut +\mathstrut 139244944q^{31} \) \(\mathstrut +\mathstrut 33554432q^{32} \) \(\mathstrut -\mathstrut 352729152q^{34} \) \(\mathstrut -\mathstrut 1123978944q^{35} \) \(\mathstrut -\mathstrut 43874954q^{37} \) \(\mathstrut +\mathstrut 925913728q^{38} \) \(\mathstrut -\mathstrut 31653888q^{40} \) \(\mathstrut -\mathstrut 899560158q^{41} \) \(\mathstrut +\mathstrut 9665476q^{43} \) \(\mathstrut +\mathstrut 1739894784q^{44} \) \(\mathstrut -\mathstrut 2412010752q^{46} \) \(\mathstrut -\mathstrut 1552169280q^{47} \) \(\mathstrut +\mathstrut 3759036333q^{49} \) \(\mathstrut +\mathstrut 3482708192q^{50} \) \(\mathstrut -\mathstrut 848586752q^{52} \) \(\mathstrut +\mathstrut 1324585278q^{53} \) \(\mathstrut +\mathstrut 5496695352q^{55} \) \(\mathstrut -\mathstrut 343408640q^{56} \) \(\mathstrut +\mathstrut 7088829504q^{58} \) \(\mathstrut -\mathstrut 4411180500q^{59} \) \(\mathstrut -\mathstrut 18975672002q^{61} \) \(\mathstrut -\mathstrut 14322308864q^{62} \) \(\mathstrut +\mathstrut 5368709120q^{64} \) \(\mathstrut +\mathstrut 16758434292q^{65} \) \(\mathstrut +\mathstrut 22397911276q^{67} \) \(\mathstrut -\mathstrut 8810108928q^{68} \) \(\mathstrut -\mathstrut 11745389568q^{70} \) \(\mathstrut +\mathstrut 25932460536q^{71} \) \(\mathstrut -\mathstrut 49990767974q^{73} \) \(\mathstrut -\mathstrut 26916324416q^{74} \) \(\mathstrut +\mathstrut 34107486208q^{76} \) \(\mathstrut +\mathstrut 28048880640q^{77} \) \(\mathstrut -\mathstrut 99679070720q^{79} \) \(\mathstrut +\mathstrut 2447376384q^{80} \) \(\mathstrut -\mathstrut 9582957888q^{82} \) \(\mathstrut -\mathstrut 37956458316q^{83} \) \(\mathstrut +\mathstrut 221618808324q^{85} \) \(\mathstrut -\mathstrut 48461612672q^{86} \) \(\mathstrut -\mathstrut 21202599936q^{88} \) \(\mathstrut +\mathstrut 210662658q^{89} \) \(\mathstrut +\mathstrut 1974242000q^{91} \) \(\mathstrut +\mathstrut 1083187200q^{92} \) \(\mathstrut +\mathstrut 80498586624q^{94} \) \(\mathstrut -\mathstrut 13965964680q^{95} \) \(\mathstrut -\mathstrut 280937161118q^{97} \) \(\mathstrut +\mathstrut 150071184672q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(18))\) 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
18.12.a.a \(1\) \(13.830\) \(\Q\) None \(-32\) \(0\) \(-3630\) \(32936\) \(+\) \(-\) \(q-2^{5}q^{2}+2^{10}q^{4}-3630q^{5}+32936q^{7}+\cdots\)
18.12.a.b \(1\) \(13.830\) \(\Q\) None \(-32\) \(0\) \(5280\) \(-49036\) \(+\) \(+\) \(q-2^{5}q^{2}+2^{10}q^{4}+5280q^{5}-49036q^{7}+\cdots\)
18.12.a.c \(1\) \(13.830\) \(\Q\) None \(32\) \(0\) \(-5766\) \(72464\) \(-\) \(-\) \(q+2^{5}q^{2}+2^{10}q^{4}-5766q^{5}+72464q^{7}+\cdots\)
18.12.a.d \(1\) \(13.830\) \(\Q\) None \(32\) \(0\) \(-5280\) \(-49036\) \(-\) \(+\) \(q+2^{5}q^{2}+2^{10}q^{4}-5280q^{5}-49036q^{7}+\cdots\)
18.12.a.e \(1\) \(13.830\) \(\Q\) None \(32\) \(0\) \(11730\) \(-50008\) \(-\) \(-\) \(q+2^{5}q^{2}+2^{10}q^{4}+11730q^{5}-50008q^{7}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(18))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(18)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)