Properties

Label 2.30
Level 2
Weight 30
Dimension 2
Nonzero newspaces 1
Newforms 2
Sturm bound 7
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 30 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 2 \)
Sturm bound: \(7\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{30}(\Gamma_1(2))\).

Total New Old
Modular forms 8 2 6
Cusp forms 6 2 4
Eisenstein series 2 0 2

Trace form

\( 2q + 1990440q^{3} + 536870912q^{4} + 12717698220q^{5} + 124117843968q^{6} + 2336537360080q^{7} - 106585334980614q^{9} + O(q^{10}) \) \( 2q + 1990440q^{3} + 536870912q^{4} + 12717698220q^{5} + 124117843968q^{6} + 2336537360080q^{7} - 106585334980614q^{9} - 9601265172480q^{10} + 1570988620558584q^{11} + 534304669040640q^{12} - 11092528397458820q^{13} - 8658937335250944q^{14} + 10437215130445680q^{15} + 144115188075855872q^{16} + 87866546144448420q^{17} + 247049121347665920q^{18} - 4477051823515048760q^{19} + 3413881120956088320q^{20} + 323530636305489984q^{21} + 51200554907593605120q^{22} - 95907354703812009360q^{23} + 33317630043286929408q^{24} - 291487399212667482850q^{25} + 706133570096965091328q^{26} - 185565836660000868720q^{27} + 627209471714110996480q^{28} - 2555257587077173639140q^{29} + 779691270526080122880q^{30} + 169166581849494746944q^{31} + 13400407582651610552160q^{33} - 18998464053346465480704q^{34} + 15012542783195751598560q^{35} - 28611282998433870249984q^{36} + 18088105620268138813420q^{37} - 74118708338195567738880q^{38} + 152209748625073150210992q^{39} - 2577319994751587450880q^{40} + 26593814015979466568724q^{41} + 136385442127117591511040q^{42} - 865229292465291154625480q^{43} + 421709046730454470754304q^{44} - 682178227204430521550340q^{45} + 1769728347835643449049088q^{46} + 998249982188035700256480q^{47} + 143426317476853280931840q^{48} - 3570452184086812928260686q^{49} - 122105992993796888985600q^{50} - 4304760864279158031767856q^{51} - 2977627918564807587921920q^{52} + 26074981958386252391645580q^{53} - 14886957230892313498091520q^{54} + 9074021667830402435695440q^{55} - 2324365792063512027070464q^{56} - 21590970399735234643559520q^{57} - 35513498882505347495362560q^{58} + 49041446699913876612175320q^{59} + 2801718602911285594030080q^{60} - 27848119893603351461348516q^{61} + 147333983768781360086384640q^{62} - 128504847187810963788735600q^{63} + 38685626227668133590597632q^{64} - 83164030562052343270687320q^{65} + 148449676496132250645037056q^{66} - 367875641163928062259190360q^{67} + 23586496381430053491179520q^{68} + 313690154866925031921776832q^{69} - 66277733357573469414359040q^{70} + 270407262189016411897648464q^{71} + 66316743543360035770859520q^{72} + 1107225994900076724981834580q^{73} - 1947095847566123849087975424q^{74} - 318323468699684350554335400q^{75} - 1201799447780893636752834560q^{76} + 1009547237855384554720201920q^{77} + 14367897208700143958753280q^{78} + 2042244860690974310098032160q^{79} + 916406735433638724155473920q^{80} + 3688634504504320503801826482q^{81} + 4715128091077280318367989760q^{82} - 19254028694951877925883196600q^{83} + 86847093886634359158472704q^{84} + 898493890263434618998446360q^{85} + 7292895364293136107970756608q^{86} - 10753320478710149773229042640q^{87} + 13744044304072927253071134720q^{88} + 24020566427012643326985883380q^{89} + 2082625117731129163052482560q^{90} - 24347948301454207535800248736q^{91} - 25744934493671521670827868160q^{92} + 34230133338133394847024656640q^{93} - 45362773861560443655614889984q^{94} - 27143376553139339894582408400q^{95} + 8943633213509026634476290048q^{96} + 130930662883674339980685698500q^{97} - 20231930582405390618087915520q^{98} - 60161478645516500791725626088q^{99} + O(q^{100}) \)

Decomposition of \(S_{30}^{\mathrm{new}}(\Gamma_1(2))\)

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
2.30.a \(\chi_{2}(1, \cdot)\) 2.30.a.a 1 1
2.30.a.b 1

Decomposition of \(S_{30}^{\mathrm{old}}(\Gamma_1(2))\) into lower level spaces

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