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Properties

Label 21.11
Level 21
Weight 11
Dimension 110
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 352
Trace bound 1

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Defining parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(352\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(21))\).

Total New Old
Modular forms 172 118 54
Cusp forms 148 110 38
Eisenstein series 24 8 16

Trace form

\( 110 q + 348 q^{3} + 2874 q^{4} - 6666 q^{5} + 25914 q^{6} + 14478 q^{7} + 79266 q^{8} + 76158 q^{9} + O(q^{10}) \) \( 110 q + 348 q^{3} + 2874 q^{4} - 6666 q^{5} + 25914 q^{6} + 14478 q^{7} + 79266 q^{8} + 76158 q^{9} + 586188 q^{10} + 295530 q^{11} - 1542498 q^{12} + 1241390 q^{13} + 3388920 q^{14} - 485052 q^{15} - 1798846 q^{16} - 4435728 q^{17} + 2548068 q^{18} + 22138106 q^{19} - 25281378 q^{21} + 10402644 q^{22} + 32492064 q^{23} + 58555650 q^{24} - 45207292 q^{25} - 76245750 q^{26} - 78968220 q^{27} + 140669546 q^{28} + 140217612 q^{29} + 182498064 q^{30} + 3879158 q^{31} - 408929322 q^{32} - 248354616 q^{33} + 17265696 q^{34} + 383046510 q^{35} - 319445754 q^{36} + 486364620 q^{37} - 555542466 q^{38} - 26647326 q^{39} - 1393767984 q^{40} + 14147208 q^{42} + 962419356 q^{43} + 997079160 q^{44} - 772750368 q^{45} - 2595104556 q^{46} - 248337618 q^{47} + 2426966358 q^{48} + 2315739320 q^{49} + 3020550726 q^{50} - 1083546582 q^{51} + 189654584 q^{52} - 2310202308 q^{53} - 1796056500 q^{54} - 945001764 q^{55} + 3213876978 q^{56} + 2241523440 q^{57} + 1491513408 q^{58} + 1714411020 q^{59} + 3682993596 q^{60} - 3824724874 q^{61} - 2421148680 q^{63} - 4498504314 q^{64} - 3892533282 q^{65} - 2866316616 q^{66} - 5983271738 q^{67} + 3075770052 q^{68} + 1301284404 q^{69} + 8584783140 q^{70} + 3681879528 q^{71} + 6327909246 q^{72} + 7658322992 q^{73} + 2594491218 q^{74} - 18853304520 q^{75} - 20750579476 q^{76} - 16773278184 q^{77} - 998832504 q^{78} - 11035674710 q^{79} + 33625283808 q^{80} + 15734944494 q^{81} + 80844750540 q^{82} - 52043620590 q^{84} - 57687211728 q^{85} - 49195564782 q^{86} - 18634861860 q^{87} + 735695400 q^{88} + 17113537596 q^{89} + 102943061508 q^{90} + 20667464180 q^{91} - 44388439284 q^{92} - 1495460022 q^{93} + 9323909052 q^{94} + 4059358662 q^{95} - 95474130522 q^{96} - 63941677720 q^{97} - 22396214502 q^{98} + 53800949412 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(21))\)

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
21.11.b \(\chi_{21}(8, \cdot)\) 21.11.b.a 20 1
21.11.d \(\chi_{21}(13, \cdot)\) 21.11.d.a 14 1
21.11.f \(\chi_{21}(10, \cdot)\) 21.11.f.a 12 2
21.11.f.b 14
21.11.h \(\chi_{21}(2, \cdot)\) 21.11.h.a 2 2
21.11.h.b 48

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(21))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(21)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)