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Properties

Label 18.12.a
Level $18$
Weight $12$
Character orbit 18.a
Rep. character $\chi_{18}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $5$
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: \(\Q\)
Newform subspaces: \( 5 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(18))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
18.12.a.a 18.a 1.a $1$ $13.830$ \(\Q\) None \(-32\) \(0\) \(-3630\) \(32936\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{5}q^{2}+2^{10}q^{4}-3630q^{5}+32936q^{7}+\cdots\)
18.12.a.b 18.a 1.a $1$ $13.830$ \(\Q\) None \(-32\) \(0\) \(5280\) \(-49036\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2^{5}q^{2}+2^{10}q^{4}+5280q^{5}-49036q^{7}+\cdots\)
18.12.a.c 18.a 1.a $1$ $13.830$ \(\Q\) None \(32\) \(0\) \(-5766\) \(72464\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{5}q^{2}+2^{10}q^{4}-5766q^{5}+72464q^{7}+\cdots\)
18.12.a.d 18.a 1.a $1$ $13.830$ \(\Q\) None \(32\) \(0\) \(-5280\) \(-49036\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{5}q^{2}+2^{10}q^{4}-5280q^{5}-49036q^{7}+\cdots\)
18.12.a.e 18.a 1.a $1$ $13.830$ \(\Q\) None \(32\) \(0\) \(11730\) \(-50008\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{5}q^{2}+2^{10}q^{4}+11730q^{5}-50008q^{7}+\cdots\)

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

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