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Properties

Label 21.18
Level 21
Weight 18
Dimension 192
Nonzero newspaces 4
Newform subspaces 9
Sturm bound 576
Trace bound 1

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 18 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 9 \)
Sturm bound: \(576\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(21))\).

Total New Old
Modular forms 284 204 80
Cusp forms 260 192 68
Eisenstein series 24 12 12

Trace form

\( 192 q - 1596 q^{2} - 6564 q^{3} - 698414 q^{4} - 2289906 q^{5} + 4960116 q^{6} - 50397326 q^{7} + 238954278 q^{8} + 40710972 q^{9} + O(q^{10}) \) \( 192 q - 1596 q^{2} - 6564 q^{3} - 698414 q^{4} - 2289906 q^{5} + 4960116 q^{6} - 50397326 q^{7} + 238954278 q^{8} + 40710972 q^{9} + 1551745296 q^{10} + 899235402 q^{11} - 6841812504 q^{12} + 8579855326 q^{13} - 18546627336 q^{14} - 31918630932 q^{15} + 1376577906 q^{16} + 92537967936 q^{17} - 41658733566 q^{18} + 158068860934 q^{19} - 347663688252 q^{20} + 574153249530 q^{21} - 2897544867408 q^{22} + 1879866803016 q^{23} - 2518413020424 q^{24} - 5442858860946 q^{25} - 1229764048758 q^{26} + 564859072962 q^{27} - 7627257622710 q^{28} - 13287442796904 q^{29} + 13260409171758 q^{30} + 19525108250182 q^{31} - 60163635248610 q^{32} - 24322945283316 q^{33} + 88602982181988 q^{34} + 43393479582042 q^{35} + 63082180607514 q^{36} - 44566001605576 q^{37} + 35028492016134 q^{38} + 139421918568018 q^{39} + 230096646721848 q^{40} - 12772817827956 q^{41} - 30041464591242 q^{42} + 403655922998672 q^{43} - 26343937391400 q^{44} - 562401660279384 q^{45} + 62308971574596 q^{46} + 272415532415838 q^{47} - 10746919049760 q^{48} + 1039199566947558 q^{49} + 264496561033650 q^{50} - 953655301944216 q^{51} - 2578834368433064 q^{52} - 67752032107020 q^{53} + 308658355044498 q^{54} + 2735403368059752 q^{55} - 1167461701543182 q^{56} - 6261665680744416 q^{57} + 4393158380689224 q^{58} + 772973750641020 q^{59} + 9749669672471724 q^{60} - 12569326167673358 q^{61} + 7010620740846180 q^{62} - 12538343098286166 q^{63} - 42296973632666 q^{64} + 2732152051359438 q^{65} + 14114237895237474 q^{66} - 11290024713175590 q^{67} - 14156069919985200 q^{68} - 815780679672024 q^{69} + 97102979468807184 q^{70} + 16025133414488748 q^{71} - 48981177778082202 q^{72} - 41901650391813764 q^{73} - 15595716763797402 q^{74} + 30732588573327786 q^{75} + 80188675647544072 q^{76} + 31709653602330336 q^{77} - 66569962539519216 q^{78} - 85324054504458882 q^{79} - 171235752958626936 q^{80} + 62369906860411488 q^{81} + 99355012862918472 q^{82} - 9163852298684244 q^{83} + 16647703590959436 q^{84} + 121929280951532040 q^{85} - 282364021302156330 q^{86} - 186199777341478476 q^{87} + 100721600726251692 q^{88} + 225256537946264856 q^{89} + 124211092701914712 q^{90} + 38632159994016712 q^{91} - 713661965132685408 q^{92} + 124898432283238314 q^{93} + 26111187649430136 q^{94} - 338714470554036198 q^{95} - 408868794401377788 q^{96} + 486807172162037908 q^{97} + 1378136444637480870 q^{98} + 238305712437160596 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(21))\)

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
21.18.a \(\chi_{21}(1, \cdot)\) 21.18.a.a 3 1
21.18.a.b 4
21.18.a.c 4
21.18.a.d 5
21.18.c \(\chi_{21}(20, \cdot)\) 21.18.c.a 44 1
21.18.e \(\chi_{21}(4, \cdot)\) 21.18.e.a 22 2
21.18.e.b 24
21.18.g \(\chi_{21}(5, \cdot)\) 21.18.g.a 2 2
21.18.g.b 84

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)