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Properties

Label 121.2
Level 121
Weight 2
Dimension 524
Nonzero newspaces 4
Newform subspaces 11
Sturm bound 2420
Trace bound 1

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Defining parameters

Level: \( N \) = \( 121 = 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 11 \)
Sturm bound: \(2420\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(121))\).

Total New Old
Modular forms 685 665 20
Cusp forms 526 524 2
Eisenstein series 159 141 18

Trace form

\( 524 q - 48 q^{2} - 49 q^{3} - 52 q^{4} - 51 q^{5} - 47 q^{6} - 43 q^{7} - 40 q^{8} - 38 q^{9} + O(q^{10}) \) \( 524 q - 48 q^{2} - 49 q^{3} - 52 q^{4} - 51 q^{5} - 47 q^{6} - 43 q^{7} - 40 q^{8} - 38 q^{9} - 33 q^{10} - 45 q^{11} - 73 q^{12} - 49 q^{13} - 39 q^{14} - 29 q^{15} - 16 q^{16} - 33 q^{17} - 24 q^{18} - 35 q^{19} - 17 q^{20} - 27 q^{21} - 20 q^{22} - 79 q^{23} + 5 q^{24} - 16 q^{25} + 3 q^{26} - 25 q^{27} + 9 q^{28} - 25 q^{29} + 13 q^{30} - 37 q^{31} - 8 q^{32} - 10 q^{33} - 59 q^{34} - 3 q^{35} + 44 q^{36} - 23 q^{37} + 5 q^{38} + 9 q^{39} + 35 q^{40} + 3 q^{41} + 49 q^{42} + q^{43} + 20 q^{44} - 23 q^{45} + 13 q^{46} - 23 q^{47} + 61 q^{48} + 8 q^{49} + 22 q^{50} + 13 q^{51} + 27 q^{52} + 11 q^{53} + 85 q^{54} + 10 q^{55} + 15 q^{56} + 25 q^{57} + 35 q^{58} - 5 q^{59} + 117 q^{60} - 17 q^{61} + 69 q^{62} + 41 q^{63} + 88 q^{64} + 21 q^{65} + 75 q^{66} - 23 q^{67} + 79 q^{68} + 39 q^{69} + 81 q^{70} + 23 q^{71} + 140 q^{72} + 11 q^{73} + 71 q^{74} + 61 q^{75} + 85 q^{76} + 35 q^{77} + 47 q^{78} + 45 q^{79} + 139 q^{80} + 64 q^{81} + 39 q^{82} + 41 q^{83} + 161 q^{84} + 57 q^{85} + 53 q^{86} + 65 q^{87} + 110 q^{88} - 45 q^{89} + 171 q^{90} + 73 q^{91} + 117 q^{92} + 87 q^{93} + 121 q^{94} + 65 q^{95} + 213 q^{96} + 57 q^{97} + 104 q^{98} + 90 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)

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
121.2.a \(\chi_{121}(1, \cdot)\) 121.2.a.a 1 1
121.2.a.b 1
121.2.a.c 1
121.2.a.d 1
121.2.c \(\chi_{121}(3, \cdot)\) 121.2.c.a 4 4
121.2.c.b 4
121.2.c.c 4
121.2.c.d 4
121.2.c.e 4
121.2.e \(\chi_{121}(12, \cdot)\) 121.2.e.a 100 10
121.2.g \(\chi_{121}(4, \cdot)\) 121.2.g.a 400 40

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(121))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(121)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)