Properties

Label 2.18.a
Level 2
Weight 18
Character orbit a
Rep. character \(\chi_{2}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 4
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 18 \)
Character orbit: \([\chi]\) = 2.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_0(2))\).

Total New Old
Modular forms 5 1 4
Cusp forms 3 1 2
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators.

\(2\)Dim.
\(-\)\(1\)

Trace form

\( q + 256q^{2} + 6084q^{3} + 65536q^{4} + 1255110q^{5} + 1557504q^{6} - 22465912q^{7} + 16777216q^{8} - 92125107q^{9} + O(q^{10}) \) \( q + 256q^{2} + 6084q^{3} + 65536q^{4} + 1255110q^{5} + 1557504q^{6} - 22465912q^{7} + 16777216q^{8} - 92125107q^{9} + 321308160q^{10} + 172399692q^{11} + 398721024q^{12} - 2180149426q^{13} - 5751273472q^{14} + 7636089240q^{15} + 4294967296q^{16} + 30163933458q^{17} - 23584027392q^{18} - 76275766060q^{19} + 82254888960q^{20} - 136682608608q^{21} + 44134321152q^{22} + 130466597784q^{23} + 102072582144q^{24} + 812361658975q^{25} - 558118253056q^{26} - 1346177902680q^{27} - 1472326008832q^{28} + 803134463070q^{29} + 1954838845440q^{30} + 2045336056352q^{31} + 1099511627776q^{32} + 1048879726128q^{33} + 7721966965248q^{34} - 28197190810320q^{35} - 6037511012352q^{36} + 33855367078118q^{37} - 19526596111360q^{38} - 13264029107784q^{39} + 21057251573760q^{40} + 53206442755242q^{41} - 34990747803648q^{42} + 26590357792364q^{43} + 11298386214912q^{44} - 115627143046770q^{45} + 33399449032704q^{46} - 232565394320592q^{47} + 26130581028864q^{48} + 272086688004537q^{49} + 207964584697600q^{50} + 183517371158472q^{51} - 142878272782336q^{52} - 163277861935626q^{53} - 344621543086080q^{54} + 216380577426120q^{55} - 376915458260992q^{56} - 464061760709040q^{57} + 205602422545920q^{58} + 697820734313340q^{59} + 500438744432640q^{60} - 898968337037698q^{61} + 523606030426112q^{62} + 2069674546852584q^{63} + 281474976710656q^{64} - 2736327346066860q^{65} + 268513209888768q^{66} - 2667002109080572q^{67} + 1976823543103488q^{68} + 793758780917856q^{69} - 7218480847441920q^{70} + 3910637666678472q^{71} - 1545602819162112q^{72} + 5855931724867274q^{73} + 8666973971998208q^{74} + 4942408333203900q^{75} - 4998808604508160q^{76} - 3873116309299104q^{77} - 3395591451592704q^{78} - 23821740190145200q^{79} + 5390656402882560q^{80} + 3706904974467321q^{81} + 13620849345341952q^{82} - 13915745478008556q^{83} - 8957631437733888q^{84} + 37859054522470380q^{85} + 6807131594845184q^{86} + 4886270073317880q^{87} + 2892386871017472q^{88} - 30722744829110310q^{89} - 29600548619973120q^{90} + 48979045151366512q^{91} + 8550258952372224q^{92} + 12443824566845568q^{93} - 59536740946071552q^{94} - 95734476739566600q^{95} + 6689428743389184q^{96} + 57649100896826978q^{97} + 69654192129161472q^{98} - 15882340072267044q^{99} + O(q^{100}) \)

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_0(2))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
2.18.a.a \(1\) \(3.664\) \(\Q\) None \(256\) \(6084\) \(1255110\) \(-22465912\) \(-\) \(q+2^{8}q^{2}+78^{2}q^{3}+2^{16}q^{4}+1255110q^{5}+\cdots\)

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_0(2))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_0(2)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)