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

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

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

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