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Properties

Label 3022.2
Level 3022
Weight 2
Dimension 95129
Nonzero newspaces 4
Sturm bound 1141560
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3022 = 2 \cdot 1511 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(1141560\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3022))\).

Total New Old
Modular forms 286900 95129 191771
Cusp forms 283881 95129 188752
Eisenstein series 3019 0 3019

Trace form

\( 95129 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} + O(q^{10}) \) \( 95129 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} - 6 q^{10} - 12 q^{11} - 4 q^{12} - 14 q^{13} - 8 q^{14} - 24 q^{15} - q^{16} - 18 q^{17} - 13 q^{18} - 20 q^{19} - 6 q^{20} - 32 q^{21} - 12 q^{22} - 24 q^{23} - 4 q^{24} - 31 q^{25} - 14 q^{26} - 40 q^{27} - 8 q^{28} - 30 q^{29} - 24 q^{30} - 32 q^{31} - q^{32} - 48 q^{33} - 18 q^{34} - 48 q^{35} - 13 q^{36} - 38 q^{37} - 20 q^{38} - 56 q^{39} - 6 q^{40} - 42 q^{41} - 32 q^{42} - 44 q^{43} - 12 q^{44} - 78 q^{45} - 24 q^{46} - 48 q^{47} - 4 q^{48} - 57 q^{49} - 31 q^{50} - 72 q^{51} - 14 q^{52} - 54 q^{53} - 40 q^{54} - 72 q^{55} - 8 q^{56} - 80 q^{57} - 30 q^{58} - 60 q^{59} - 24 q^{60} - 62 q^{61} - 32 q^{62} - 104 q^{63} - q^{64} - 84 q^{65} - 48 q^{66} - 68 q^{67} - 18 q^{68} - 96 q^{69} - 48 q^{70} - 72 q^{71} - 13 q^{72} - 74 q^{73} - 38 q^{74} - 124 q^{75} - 20 q^{76} - 96 q^{77} - 56 q^{78} - 80 q^{79} - 6 q^{80} - 121 q^{81} - 42 q^{82} - 84 q^{83} - 32 q^{84} - 108 q^{85} - 44 q^{86} - 120 q^{87} - 12 q^{88} - 90 q^{89} - 78 q^{90} - 112 q^{91} - 24 q^{92} - 128 q^{93} - 48 q^{94} - 120 q^{95} - 4 q^{96} - 98 q^{97} - 57 q^{98} - 156 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3022))\)

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
3022.2.a \(\chi_{3022}(1, \cdot)\) 3022.2.a.a 28 1
3022.2.a.b 28
3022.2.a.c 34
3022.2.a.d 35
3022.2.c \(\chi_{3022}(631, \cdot)\) n/a 504 4
3022.2.e \(\chi_{3022}(3, \cdot)\) n/a 18900 150
3022.2.g \(\chi_{3022}(5, \cdot)\) n/a 75600 600

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3022))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3022)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1511))\)\(^{\oplus 2}\)