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Properties

Label 18.4.a
Level $18$
Weight $4$
Character orbit 18.a
Rep. character $\chi_{18}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(18))\) 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
18.4.a.a 18.a 1.a $1$ $1.062$ \(\Q\) None \(2\) \(0\) \(-6\) \(-16\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}-6q^{5}-2^{4}q^{7}+8q^{8}+\cdots\)

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

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