Properties

Label 18.22.a
Level $18$
Weight $22$
Character orbit 18.a
Rep. character $\chi_{18}(1,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $7$
Sturm bound $66$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 18.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(66\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_0(18))\).

Total New Old
Modular forms 67 9 58
Cusp forms 59 9 50
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
\(+\)\(+\)$+$\(2\)
\(+\)\(-\)$-$\(3\)
\(-\)\(+\)$-$\(2\)
\(-\)\(-\)$+$\(2\)
Plus space\(+\)\(4\)
Minus space\(-\)\(5\)

Trace form

\( 9 q - 1024 q^{2} + 9437184 q^{4} + 7564746 q^{5} + 33088032 q^{7} - 1073741824 q^{8} + O(q^{10}) \) \( 9 q - 1024 q^{2} + 9437184 q^{4} + 7564746 q^{5} + 33088032 q^{7} - 1073741824 q^{8} + 28087547904 q^{10} + 118432139244 q^{11} + 487259895726 q^{13} - 319510003712 q^{14} + 9895604649984 q^{16} - 15931512333162 q^{17} - 6378860142324 q^{19} + 7932211101696 q^{20} + 19326219522048 q^{22} - 616891763729976 q^{23} + 1971442355939703 q^{25} - 1201730472163328 q^{26} + 34695316242432 q^{28} - 5678451945269598 q^{29} + 6545023913467656 q^{31} - 1125899906842624 q^{32} - 849178585626624 q^{34} - 60517383765632544 q^{35} + 78028834408175142 q^{37} + 31451692857364480 q^{38} + 29451928630984704 q^{40} - 85304346201644514 q^{41} + 4086616581354996 q^{43} + 124185098839916544 q^{44} - 763876484804026368 q^{46} + 1200258981702208608 q^{47} + 106669981806884577 q^{49} + 1296984820296958976 q^{50} + 510929032420786176 q^{52} + 1257332649228262314 q^{53} - 1243912472899801128 q^{55} - 335030521652314112 q^{56} + 4564158137867704320 q^{58} + 1083312742821035340 q^{59} + 8212326444944506494 q^{61} - 12943049292331409408 q^{62} + 10376293541461622784 q^{64} - 26761482555979462068 q^{65} + 68018217301900426572 q^{67} - 16705401476257677312 q^{68} + 26847453515934892032 q^{70} + 65202670606953312504 q^{71} - 134977546236419661654 q^{73} + 37566018964703488000 q^{74} - 6688719652597530624 q^{76} + 154848587197824987456 q^{77} - 99915463965187649160 q^{79} + 8317526188171984896 q^{80} - 100595891313103214592 q^{82} + 177294054105498031764 q^{83} + 42697757675515846572 q^{85} - 54229059086812712960 q^{86} + 20265009961551003648 q^{88} - 208548149496467513346 q^{89} + 314563364040235655808 q^{91} - 646857898044923314176 q^{92} + 667823528954292240384 q^{94} - 874641586845937220904 q^{95} - 1857462076676411793918 q^{97} - 2768540499272291017728 q^{98} + O(q^{100}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_0(18))\) 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
18.22.a.a 18.a 1.a $1$ $50.306$ \(\Q\) None \(-1024\) \(0\) \(-12954174\) \(-479513104\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{10}q^{2}+2^{20}q^{4}-12954174q^{5}+\cdots\)
18.22.a.b 18.a 1.a $1$ $50.306$ \(\Q\) None \(-1024\) \(0\) \(-4975350\) \(1427425832\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{10}q^{2}+2^{20}q^{4}-4975350q^{5}+\cdots\)
18.22.a.c 18.a 1.a $1$ $50.306$ \(\Q\) None \(-1024\) \(0\) \(23245050\) \(-1322977768\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{10}q^{2}+2^{20}q^{4}+23245050q^{5}+\cdots\)
18.22.a.d 18.a 1.a $1$ $50.306$ \(\Q\) None \(1024\) \(0\) \(-26444550\) \(166115864\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{10}q^{2}+2^{20}q^{4}-26444550q^{5}+\cdots\)
18.22.a.e 18.a 1.a $1$ $50.306$ \(\Q\) None \(1024\) \(0\) \(28693770\) \(-853202392\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{10}q^{2}+2^{20}q^{4}+28693770q^{5}+\cdots\)
18.22.a.f 18.a 1.a $2$ $50.306$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(-2048\) \(0\) \(-15247776\) \(547619800\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2^{10}q^{2}+2^{20}q^{4}+(-7623888+\cdots)q^{5}+\cdots\)
18.22.a.g 18.a 1.a $2$ $50.306$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(2048\) \(0\) \(15247776\) \(547619800\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{10}q^{2}+2^{20}q^{4}+(7623888-\beta )q^{5}+\cdots\)

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_0(18))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_0(18)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)