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Properties

Label 21.28
Level 21
Weight 28
Dimension 310
Nonzero newspaces 4
Newform subspaces 9
Sturm bound 896
Trace bound 1

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 28 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 9 \)
Sturm bound: \(896\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{28}(\Gamma_1(21))\).

Total New Old
Modular forms 444 322 122
Cusp forms 420 310 110
Eisenstein series 24 12 12

Trace form

\( 310 q - 49500 q^{2} + 3188643 q^{3} - 414937742 q^{4} + 5982965976 q^{5} - 19648436652 q^{6} - 540590151974 q^{7} + 775483326774 q^{8} - 33791676960417 q^{9} + O(q^{10}) \) \( 310 q - 49500 q^{2} + 3188643 q^{3} - 414937742 q^{4} + 5982965976 q^{5} - 19648436652 q^{6} - 540590151974 q^{7} + 775483326774 q^{8} - 33791676960417 q^{9} - 139896557760912 q^{10} + 95901690115296 q^{11} + 2651753881881744 q^{12} - 1930614877400644 q^{13} + 15180352603066920 q^{14} + 7825387036115322 q^{15} - 1052688807316430 q^{16} + 17483772167020068 q^{17} + 230009439382741170 q^{18} - 323678405243754034 q^{19} - 2543725154215806876 q^{20} - 639369305487350007 q^{21} + 3348313627386422592 q^{22} - 6933488543328968808 q^{23} + 27502404210741768624 q^{24} - 32465024624427035906 q^{25} + 60093190484817657978 q^{26} - 16210220612075905068 q^{27} + 310796071907169639850 q^{28} - 131584448306877146136 q^{29} + 442517035726717461990 q^{30} + 835594254610060295090 q^{31} - 1866055282591721373138 q^{32} + 1104370494532388573679 q^{33} - 565780068799221777468 q^{34} - 1330006744291583887116 q^{35} + 22328786361535829612106 q^{36} - 4131148522480523935618 q^{37} - 7033596989271481427850 q^{38} + 8254908422009558955948 q^{39} - 53734642179005333426424 q^{40} + 13283440601731361742000 q^{41} - 28003570400064725314578 q^{42} + 24188792261037760295552 q^{43} - 70355040803808529520424 q^{44} + 20497423158874202089671 q^{45} + 64292129330071753121892 q^{46} - 77760301118829529002408 q^{47} + 167931083798231302461024 q^{48} + 114034864471916701402606 q^{49} + 735511420179156171573522 q^{50} - 70101044921874300320205 q^{51} - 215274738843546140866120 q^{52} - 427600815002731480306980 q^{53} - 729176349356730410415750 q^{54} - 581330289559991158142940 q^{55} + 2666428050486616360167570 q^{56} + 1639271839729236201887850 q^{57} + 5900720158725161565299688 q^{58} - 2665635499933115568083472 q^{59} + 1941973000657437570216660 q^{60} + 5572381850722406195491058 q^{61} - 20659547422793192677604988 q^{62} - 1824355881742918620023157 q^{63} - 4247702664613820134766138 q^{64} - 20732151946252638913781256 q^{65} - 9346216744273596309842022 q^{66} + 49983838800780360467548118 q^{67} + 7221370154534195790696384 q^{68} - 36474298841830981006153080 q^{69} + 37305295274433683993384976 q^{70} + 86471678796642361170281748 q^{71} - 25033402182269057479411410 q^{72} - 51558498707799650837504566 q^{73} + 169593634553611694920828998 q^{74} + 83512335388966242217008096 q^{75} - 313440849613236694602831160 q^{76} - 37974005723040706108863540 q^{77} + 84233125922723356228814304 q^{78} + 227063358703526342663927714 q^{79} - 98724902971834480246415784 q^{80} - 315641205046545595303925349 q^{81} + 319842853844228271464293368 q^{82} + 156850343024962041137590440 q^{83} + 238672595022013619516685612 q^{84} - 720494434607936309860529892 q^{85} - 681555076991599814544682170 q^{86} + 2063381226526773263910706056 q^{87} - 789792659245745497378980372 q^{88} - 1926314809510512984665439912 q^{89} + 78028192213219640574800280 q^{90} + 590356442120688762961254980 q^{91} - 2554494370886037835658102784 q^{92} - 2152052794697749391669302473 q^{93} + 1487150301816565690969247688 q^{94} - 1224896143044207675928180416 q^{95} + 6337869209248610409352250292 q^{96} + 5519242538236140838593223100 q^{97} - 6643688228126667224512449882 q^{98} + 10056776188990520397465199458 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{28}^{\mathrm{new}}(\Gamma_1(21))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
21.28.a \(\chi_{21}(1, \cdot)\) 21.28.a.a 6 1
21.28.a.b 7
21.28.a.c 7
21.28.a.d 8
21.28.c \(\chi_{21}(20, \cdot)\) 21.28.c.a 2 1
21.28.c.b 68
21.28.e \(\chi_{21}(4, \cdot)\) 21.28.e.a 34 2
21.28.e.b 38
21.28.g \(\chi_{21}(5, \cdot)\) 21.28.g.a 140 2

Decomposition of \(S_{28}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{28}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{28}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)