Properties

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

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Defining parameters

Level: \( N \) = \( 121 = 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newforms: \( 11 \)
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

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

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 the 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

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