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Properties

Label 18.10.a
Level $18$
Weight $10$
Character orbit 18.a
Rep. character $\chi_{18}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $4$
Sturm bound $30$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 18.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(30\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(18))\).

Total New Old
Modular forms 31 4 27
Cusp forms 23 4 19
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
\(+\)\(+\)$+$\(1\)
\(+\)\(-\)$-$\(1\)
\(-\)\(+\)$-$\(1\)
\(-\)\(-\)$+$\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(2\)

Trace form

\( 4 q + 1024 q^{4} - 3564 q^{5} + 7208 q^{7} + O(q^{10}) \) \( 4 q + 1024 q^{4} - 3564 q^{5} + 7208 q^{7} - 16896 q^{10} + 26568 q^{11} - 72352 q^{13} - 41472 q^{14} + 262144 q^{16} + 349596 q^{17} - 837352 q^{19} - 912384 q^{20} + 1528320 q^{22} + 908496 q^{23} + 496948 q^{25} - 3566592 q^{26} + 1845248 q^{28} + 6197796 q^{29} - 16588648 q^{31} + 12340224 q^{34} + 10375776 q^{35} + 7630136 q^{37} - 19367424 q^{38} - 4325376 q^{40} - 27730836 q^{41} + 35353736 q^{43} + 6801408 q^{44} - 19716096 q^{46} + 31547232 q^{47} - 79456380 q^{49} + 104011776 q^{50} - 18522112 q^{52} - 73867788 q^{53} + 100438992 q^{55} - 10616832 q^{56} - 180045312 q^{58} - 145822680 q^{59} + 464275736 q^{61} + 23763456 q^{62} + 67108864 q^{64} - 34202088 q^{65} - 666162424 q^{67} + 89496576 q^{68} + 211418112 q^{70} + 306248688 q^{71} - 64987264 q^{73} - 115623936 q^{74} - 214362112 q^{76} + 51378624 q^{77} + 289293560 q^{79} - 233570304 q^{80} + 410661888 q^{82} + 439073784 q^{83} - 137951208 q^{85} - 838937088 q^{86} + 391249920 q^{88} - 658833588 q^{89} - 1214045552 q^{91} + 232574976 q^{92} + 787934208 q^{94} + 2136975696 q^{95} + 151355744 q^{97} + 186458112 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(18))\) 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
18.10.a.a 18.a 1.a $1$ $9.271$ \(\Q\) None \(-16\) \(0\) \(-870\) \(-952\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{4}q^{2}+2^{8}q^{4}-870q^{5}-952q^{7}+\cdots\)
18.10.a.b 18.a 1.a $1$ $9.271$ \(\Q\) None \(-16\) \(0\) \(-384\) \(5852\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2^{4}q^{2}+2^{8}q^{4}-384q^{5}+5852q^{7}+\cdots\)
18.10.a.c 18.a 1.a $1$ $9.271$ \(\Q\) None \(16\) \(0\) \(-2694\) \(-3544\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{4}q^{2}+2^{8}q^{4}-2694q^{5}-3544q^{7}+\cdots\)
18.10.a.d 18.a 1.a $1$ $9.271$ \(\Q\) None \(16\) \(0\) \(384\) \(5852\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{4}q^{2}+2^{8}q^{4}+384q^{5}+5852q^{7}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(18))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(18)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)