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Properties

Label 121.6
Level 121
Weight 6
Dimension 2905
Nonzero newspaces 4
Sturm bound 7260
Trace bound 1

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Defining parameters

Level: \( N \) = \( 121 = 11^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(7260\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(121))\).

Total New Old
Modular forms 3105 3046 59
Cusp forms 2945 2905 40
Eisenstein series 160 141 19

Trace form

\( 2905 q - 45 q^{2} - 45 q^{3} - 45 q^{4} - 45 q^{5} - 5 q^{6} - 635 q^{7} - 365 q^{8} + 1055 q^{9} + O(q^{10}) \) \( 2905 q - 45 q^{2} - 45 q^{3} - 45 q^{4} - 45 q^{5} - 5 q^{6} - 635 q^{7} - 365 q^{8} + 1055 q^{9} + 1965 q^{10} + 395 q^{11} + 555 q^{12} - 1055 q^{13} + 945 q^{14} - 7525 q^{15} - 16325 q^{16} - 3555 q^{17} + 5545 q^{18} + 4425 q^{19} + 17325 q^{20} + 17605 q^{21} + 12520 q^{22} + 20305 q^{23} + 2735 q^{24} - 25785 q^{25} - 65935 q^{26} - 46905 q^{27} - 64835 q^{28} - 8495 q^{29} + 42585 q^{30} + 50555 q^{31} + 152625 q^{32} + 42560 q^{33} + 8675 q^{34} - 37955 q^{35} - 137535 q^{36} - 68905 q^{37} - 120935 q^{38} - 61975 q^{39} - 66775 q^{40} + 20625 q^{41} + 234245 q^{42} + 109165 q^{43} + 92805 q^{44} + 157255 q^{45} - 37675 q^{46} - 60655 q^{47} - 190335 q^{48} - 128195 q^{49} - 125985 q^{50} - 85155 q^{51} + 195125 q^{52} - 18195 q^{53} - 93955 q^{54} - 12310 q^{55} - 60585 q^{56} + 28145 q^{57} - 5655 q^{58} - 121265 q^{59} - 56255 q^{60} + 59825 q^{61} + 295125 q^{62} + 39425 q^{63} - 52085 q^{64} + 54225 q^{65} - 15875 q^{66} + 163805 q^{67} + 235325 q^{68} + 165955 q^{69} + 452705 q^{70} + 228095 q^{71} + 226395 q^{72} - 31255 q^{73} - 822235 q^{74} - 532335 q^{75} - 569795 q^{76} - 393655 q^{77} - 834145 q^{78} - 429275 q^{79} + 525745 q^{80} + 801305 q^{81} + 1130975 q^{82} + 585285 q^{83} - 148175 q^{84} + 106265 q^{85} - 564245 q^{86} - 28855 q^{87} - 120450 q^{88} - 118015 q^{89} + 490205 q^{90} + 759065 q^{91} + 909005 q^{92} + 614855 q^{93} + 317885 q^{94} + 39185 q^{95} - 657535 q^{96} - 1121825 q^{97} - 1628055 q^{98} - 726350 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(121))\)

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
121.6.a \(\chi_{121}(1, \cdot)\) 121.6.a.a 1 1
121.6.a.b 1
121.6.a.c 2
121.6.a.d 3
121.6.a.e 5
121.6.a.f 5
121.6.a.g 8
121.6.a.h 8
121.6.a.i 8
121.6.c \(\chi_{121}(3, \cdot)\) n/a 164 4
121.6.e \(\chi_{121}(12, \cdot)\) n/a 540 10
121.6.g \(\chi_{121}(4, \cdot)\) n/a 2160 40

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(121))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(121)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)