Properties

Label 21.30
Level 21
Weight 30
Dimension 332
Nonzero newspaces 4
Newform subspaces 9
Sturm bound 960
Trace bound 1

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 30 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 9 \)
Sturm bound: \(960\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{30}(\Gamma_1(21))\).

Total New Old
Modular forms 476 344 132
Cusp forms 452 332 120
Eisenstein series 24 12 12

Trace form

\( 332q + 67332q^{2} - 4782972q^{3} - 6782104686q^{4} - 35019763866q^{5} - 69391314252q^{6} + 600575102106q^{7} + 13013524033926q^{8} - 376055722691160q^{9} + O(q^{10}) \) \( 332q + 67332q^{2} - 4782972q^{3} - 6782104686q^{4} - 35019763866q^{5} - 69391314252q^{6} + 600575102106q^{7} + 13013524033926q^{8} - 376055722691160q^{9} + 87292716968016q^{10} - 3595645323983670q^{11} - 22502857319849640q^{12} + 94346798555795750q^{13} + 28711913782546968q^{14} - 253826294709043332q^{15} - 2485399798709107726q^{16} - 2744692590173794536q^{17} + 3603267176782339746q^{18} - 15261854574353427850q^{19} + 13421225335151298948q^{20} + 58647440769479251914q^{21} - 52945672033200769776q^{22} + 302563028626723984104q^{23} - 689646173299762162104q^{24} + 99412842535930896194q^{25} + 1426519810171841258538q^{26} + 218837978263024718418q^{27} - 5917316204691796475254q^{28} + 6402305415994915482480q^{29} + 6341911433390945192958q^{30} - 10946377093105059267658q^{31} + 5149429396066367957886q^{32} - 21564411272956788095916q^{33} + 62834954416870544527524q^{34} - 77170527249937196355558q^{35} + 473938274273332113459258q^{36} + 129070757043563314712784q^{37} - 84683593832511087121242q^{38} + 188664057505206120391770q^{39} + 73457013275780370964248q^{40} - 1045320617608182843278652q^{41} + 2498809111659106824894534q^{42} + 727361367777694903228752q^{43} + 1209354416125997846381784q^{44} + 2760925276483150679885736q^{45} - 10978814388967196936118012q^{46} + 10758810193265525607174414q^{47} - 7880742082207161510391584q^{48} + 28109866447885648326769682q^{49} + 25393569178242290430788850q^{50} - 5487700696258774843454904q^{51} + 23445190768660609934651288q^{52} - 20577129121603015548290148q^{53} - 78243667937994843752509566q^{54} + 60535438062869222175842232q^{55} + 95032044533860106591805618q^{56} - 100842266462367789951214752q^{57} - 78741546558559168273940472q^{58} + 280011363360880812337964028q^{59} - 383704785228576390724941156q^{60} - 681670025366562468217294678q^{61} + 2685384119675348746529211684q^{62} - 698695976675698273965321678q^{63} - 1633756768694482172760054618q^{64} + 1239660796309154286631752558q^{65} - 184978839174612590418700878q^{66} - 687782292138893536382222054q^{67} - 877426149644441006962520976q^{68} + 1298504087682140691145312488q^{69} + 1016290036108567631113027344q^{70} - 3206744848806023555452190292q^{71} + 931696934906707173852088086q^{72} + 7366662052746525545065319444q^{73} - 12585300712519656238104846426q^{74} - 2725067073920340550857683334q^{75} + 31245757574685864521805146504q^{76} + 4607462446519169494367881536q^{77} - 3680585942701219191708919056q^{78} + 2382244591906471168803133966q^{79} - 357680135136312292589400216q^{80} + 25240382389753293817665412740q^{81} + 4231440912992043646979617896q^{82} - 4701371689262823400496027412q^{83} - 24895642058110223902106913012q^{84} + 57290061770161934132444899320q^{85} + 16249133903685711987224205942q^{86} - 45789246090360328893173768196q^{87} - 126186091674310468570661256660q^{88} + 32554759052988359973875982576q^{89} + 19586748692816577703798085592q^{90} - 88886248260995897012938494280q^{91} - 269165926366336449524580240672q^{92} + 307874245708300297845164283426q^{93} + 285765727266488782322066210904q^{94} - 381443550810248707034203236918q^{95} - 123296520704949925510380438492q^{96} + 39676676633328584872052798684q^{97} - 30646118055466716573047552346q^{98} - 201874491876496158814086934236q^{99} + O(q^{100}) \)

Decomposition of \(S_{30}^{\mathrm{new}}(\Gamma_1(21))\)

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
21.30.a \(\chi_{21}(1, \cdot)\) 21.30.a.a 6 1
21.30.a.b 7
21.30.a.c 7
21.30.a.d 8
21.30.c \(\chi_{21}(20, \cdot)\) 21.30.c.a 76 1
21.30.e \(\chi_{21}(4, \cdot)\) 21.30.e.a 38 2
21.30.e.b 40
21.30.g \(\chi_{21}(5, \cdot)\) 21.30.g.a 2 2
21.30.g.b 148

Decomposition of \(S_{30}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{30}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{30}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{30}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{30}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)