Properties

Label 7.18.a
Level 7
Weight 18
Character orbit a
Rep. character \(\chi_{7}(1,\cdot)\)
Character field \(\Q\)
Dimension 9
Newforms 2
Sturm bound 12
Trace bound 1

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 18 \)
Character orbit: \([\chi]\) = 7.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_0(7))\).

Total New Old
Modular forms 13 9 4
Cusp forms 11 9 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.

\(7\)Dim.
\(+\)\(4\)
\(-\)\(5\)

Trace form

\( 9q + 783q^{2} - 4556q^{3} + 518377q^{4} + 1887546q^{5} - 12914050q^{6} + 5764801q^{7} + 50565375q^{8} + 550607101q^{9} + O(q^{10}) \) \( 9q + 783q^{2} - 4556q^{3} + 518377q^{4} + 1887546q^{5} - 12914050q^{6} + 5764801q^{7} + 50565375q^{8} + 550607101q^{9} - 1238976556q^{10} + 1376056092q^{11} + 1808004758q^{12} - 7906717126q^{13} + 2369333211q^{14} + 10511459848q^{15} + 68756018977q^{16} - 38906747382q^{17} - 57745166281q^{18} - 124371715948q^{19} + 696629307192q^{20} + 5857037816q^{21} - 165827773384q^{22} - 57454446456q^{23} - 3364741774638q^{24} + 1558855502383q^{25} + 1306870396608q^{26} - 1979560213640q^{27} + 3176272760577q^{28} + 4557180676038q^{29} - 8345669499568q^{30} - 9031654556672q^{31} + 8993367678783q^{32} - 8668173848912q^{33} + 9550289394210q^{34} + 7713891747702q^{35} + 36029826665369q^{36} - 36618912510482q^{37} - 2290065612750q^{38} + 70085676306856q^{39} + 4883968756656q^{40} - 117535703958414q^{41} - 91393183492058q^{42} + 17364741180924q^{43} + 565941146283792q^{44} + 71369525819650q^{45} - 746685664899216q^{46} + 182934682708368q^{47} - 686371314511906q^{48} + 299096375126409q^{49} - 666974137177491q^{50} - 135424491709656q^{51} + 969348145597188q^{52} + 584453015524614q^{53} + 393077722989284q^{54} + 61865024116744q^{55} + 191775922721103q^{56} + 447116943026440q^{57} + 1050293289694430q^{58} - 2613865125975396q^{59} + 1229363225188448q^{60} + 421124768793074q^{61} - 8023299436345524q^{62} + 3197787303443453q^{63} + 10582028453527809q^{64} + 5734657646062380q^{65} - 4880637871780096q^{66} - 5325292938220012q^{67} - 21116927692333914q^{68} + 5480505589090992q^{69} + 3163761735795556q^{70} - 3155228056242552q^{71} + 5634015427238175q^{72} + 4116363386210314q^{73} + 35897205257421270q^{74} - 15558598962126340q^{75} - 24633092300689782q^{76} + 898361983669332q^{77} - 62221917332812552q^{78} + 45214703375651760q^{79} + 66793516782396384q^{80} + 3495137753104537q^{81} - 49098701844726254q^{82} - 14126669363175516q^{83} + 31476294232873798q^{84} - 117341825000937228q^{85} + 54905457266037600q^{86} + 132882859067191480q^{87} + 157325636327025120q^{88} - 196945226471180982q^{89} - 37797228288651388q^{90} + 52593007167711822q^{91} - 66486016223945952q^{92} + 155884043743390128q^{93} + 11452168238280708q^{94} + 270887841011710632q^{95} - 946683413302913342q^{96} + 121191804043744378q^{97} + 26021384635997583q^{98} - 387522708672295220q^{99} + O(q^{100}) \)

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_0(7))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7
7.18.a.a \(4\) \(12.826\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(186\) \(-2786\) \(274722\) \(-23059204\) \(+\) \(q+(46-\beta _{1})q^{2}+(-698-3\beta _{1}-\beta _{3})q^{3}+\cdots\)
7.18.a.b \(5\) \(12.826\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(597\) \(-1770\) \(1612824\) \(28824005\) \(-\) \(q+(119+\beta _{1})q^{2}+(-349-13\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_0(7))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_0(7)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)