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Properties

Label 18.8.a
Level $18$
Weight $8$
Character orbit 18.a
Rep. character $\chi_{18}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
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: \(\Q\)
Newform subspaces: \( 2 \)
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

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

Display 100 coefficients 10 coefficients

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

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

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