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Properties

Label 3.21
Level 3
Weight 21
Dimension 6
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 14
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 21 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(14\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{21}(\Gamma_1(3))\).

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

Trace form

\( 6 q - 4122 q^{3} - 2125200 q^{4} - 96401232 q^{6} + 559607916 q^{7} - 1087483482 q^{9} + O(q^{10}) \) \( 6 q - 4122 q^{3} - 2125200 q^{4} - 96401232 q^{6} + 559607916 q^{7} - 1087483482 q^{9} - 10880304480 q^{10} + 63957886128 q^{12} + 17847879276 q^{13} - 487764624960 q^{15} - 317472843648 q^{16} + 9564155313120 q^{18} - 14958020195124 q^{19} + 25978999888044 q^{21} - 71051286019680 q^{22} + 294048705803904 q^{24} - 397204775017050 q^{25} + 1077025592505798 q^{27} - 2034284889273504 q^{28} + 3061064118304800 q^{30} - 2182905165483348 q^{31} + 3811197222014400 q^{33} - 7566372644651136 q^{34} + 6910111676037744 q^{36} - 1934341462168404 q^{37} - 15813602040849876 q^{39} + 44482420967535360 q^{40} - 86552595699685920 q^{42} + 58194987502184076 q^{43} - 81854223046416000 q^{45} + 151411391218915776 q^{46} - 154489681080035712 q^{48} + 188165158287453522 q^{49} - 117657755976045312 q^{51} - 230547517796956704 q^{52} + 489800358305152272 q^{54} - 393208608470140800 q^{55} + 1211071992434087436 q^{57} - 1639827118548168480 q^{58} + 2591328282252814080 q^{60} - 2999109545381544468 q^{61} + 444547436097192876 q^{63} - 83569554960393216 q^{64} + 120735307117251360 q^{66} + 4488155969890198476 q^{67} - 3511312424189451648 q^{69} - 1812568842584740800 q^{70} - 10414532525611288320 q^{72} + 15738405804262597836 q^{73} - 20871070048457840250 q^{75} + 27275280223392575328 q^{76} - 13410777930056987040 q^{78} + 17679940751103803436 q^{79} - 13011625055229011514 q^{81} - 35403353112903693120 q^{82} + 60397598618988279264 q^{84} - 22576574831711316480 q^{85} + 17858271599894295360 q^{87} - 95000209108729447680 q^{88} + 179562325304911301280 q^{90} - 6461010485165713512 q^{91} - 24838278011742494484 q^{93} - 311754310853935072896 q^{94} + 184738040137761352704 q^{96} + 223240336245548394636 q^{97} - 178130031568853028480 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{21}^{\mathrm{new}}(\Gamma_1(3))\)

We only show spaces with odd 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
3.21.b \(\chi_{3}(2, \cdot)\) 3.21.b.a 6 1