Properties

Label 18.10.a
Level 18
Weight 10
Character orbit a
Rep. character \(\chi_{18}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 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: \(\Q\)
Newforms: \( 4 \)
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

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

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(18))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
18.10.a.a \(1\) \(9.271\) \(\Q\) None \(-16\) \(0\) \(-870\) \(-952\) \(+\) \(-\) \(q-2^{4}q^{2}+2^{8}q^{4}-870q^{5}-952q^{7}+\cdots\)
18.10.a.b \(1\) \(9.271\) \(\Q\) None \(-16\) \(0\) \(-384\) \(5852\) \(+\) \(+\) \(q-2^{4}q^{2}+2^{8}q^{4}-384q^{5}+5852q^{7}+\cdots\)
18.10.a.c \(1\) \(9.271\) \(\Q\) None \(16\) \(0\) \(-2694\) \(-3544\) \(-\) \(-\) \(q+2^{4}q^{2}+2^{8}q^{4}-2694q^{5}-3544q^{7}+\cdots\)
18.10.a.d \(1\) \(9.271\) \(\Q\) None \(16\) \(0\) \(384\) \(5852\) \(-\) \(+\) \(q+2^{4}q^{2}+2^{8}q^{4}+384q^{5}+5852q^{7}+\cdots\)

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

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