Properties

Label 7.30
Level 7
Weight 30
Dimension 51
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 120
Trace bound 1

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 30 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(120\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{30}(\Gamma_1(7))\).

Total New Old
Modular forms 61 55 6
Cusp forms 55 51 4
Eisenstein series 6 4 2

Trace form

\( 51q - 17283q^{2} + 5152308q^{3} + 1253646333q^{4} + 16784935524q^{5} + 617632528890q^{6} + 1036080279801q^{7} - 20586076750257q^{8} - 111020963540985q^{9} + O(q^{10}) \) \( 51q - 17283q^{2} + 5152308q^{3} + 1253646333q^{4} + 16784935524q^{5} + 617632528890q^{6} + 1036080279801q^{7} - 20586076750257q^{8} - 111020963540985q^{9} - 284125982267778q^{10} + 4542438808864572q^{11} + 12979297144737210q^{12} - 80278651136369658q^{13} + 77933429186423097q^{14} - 82422717211100688q^{15} + 1486342522810235889q^{16} + 2252377094965276944q^{17} - 16215223654965442845q^{18} + 14947197735731879604q^{19} - 61112997003183990144q^{20} + 37202035461429795138q^{21} - 47154924262875021660q^{22} - 7578109729372571676q^{23} - 574485853840853109918q^{24} - 69122049143564793399q^{25} - 545167524062048644764q^{26} + 3503682752617641445032q^{27} + 149217376323246112581q^{28} - 1644855106238432844654q^{29} - 2751970323330400952586q^{30} + 5359188114850439833236q^{31} - 7492906963519134642033q^{32} + 89132138051083485109206q^{33} - 113406687123031620674658q^{34} + 138440657739904977218958q^{35} - 127006490349007486445031q^{36} - 5061728488047031864896q^{37} + 22094433360156499947192q^{38} - 246470611841036770097232q^{39} + 482528684255578218973680q^{40} - 432596130343749348123546q^{41} - 756924363739782104174154q^{42} - 4228297635347228460300q^{43} - 1526932842074780058309564q^{44} + 2224749839337988517209410q^{45} + 969212606061771057236478q^{46} + 1378648063700843885740140q^{47} + 6795440466643650650895870q^{48} + 396462803278176354849843q^{49} + 17299220409976973651630493q^{50} - 16572186837012538574175048q^{51} - 28361792217183585952346436q^{52} + 60591989475902447535759528q^{53} - 106194138296778718073454q^{54} - 56907845072529202892637888q^{55} - 22061648422482550100160753q^{56} - 60442694753777202714534108q^{57} - 182836829139987600548639214q^{58} + 89878904385081185660398980q^{59} + 128494267294987159199878524q^{60} + 213600091987396321416258252q^{61} - 749436728150718707796330264q^{62} + 820058953851096262577638245q^{63} + 1075409060124059425963155297q^{64} - 489603951497692422749373456q^{65} - 1877533715135843491987435770q^{66} + 1109278262630382523267241268q^{67} + 1178064509348881638538048050q^{68} - 282653737994998387411961148q^{69} - 1158777196442919209969796774q^{70} + 4377248655693487184847849288q^{71} - 6158967544720753562737230657q^{72} - 8025308003467745124119867280q^{73} + 14434876696793900526963162096q^{74} - 5939521896121212124161042852q^{75} - 14294016444554015811063257262q^{76} + 418737009704362623460884894q^{77} + 40210598146949041609351232448q^{78} - 5529941070246905253384482844q^{79} - 40943059132552507809175677072q^{80} + 28733981904795703437872710245q^{81} + 17826231732535950532313650110q^{82} - 63586098908476807748155777476q^{83} + 47362224218041595509914126258q^{84} + 30181441706477353705349866200q^{85} - 65755877567339366441886725160q^{86} + 3904063630708166668867086480q^{87} + 99805347914804588036272075200q^{88} + 62018139091204712656826570544q^{89} - 99658564483508233811842295364q^{90} - 7295193392012298510882213762q^{91} + 51666231982012284672876897576q^{92} - 181904284711174919529943044222q^{93} - 90450539849297038194750768606q^{94} + 41279973451729185770357336292q^{95} - 148927033591803732737438881278q^{96} + 56399709820444099969063261134q^{97} + 40721823019008079930543096605q^{98} + 197077453432899831335084153652q^{99} + O(q^{100}) \)

Decomposition of \(S_{30}^{\mathrm{new}}(\Gamma_1(7))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
7.30.a \(\chi_{7}(1, \cdot)\) 7.30.a.a 7 1
7.30.a.b 8
7.30.c \(\chi_{7}(2, \cdot)\) 7.30.c.a 36 2

Decomposition of \(S_{30}^{\mathrm{old}}(\Gamma_1(7))\) into lower level spaces

\( S_{30}^{\mathrm{old}}(\Gamma_1(7)) \cong \) \(S_{30}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)