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

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

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