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Properties

Label 151.2
Level 151
Weight 2
Dimension 876
Nonzero newspaces 6
Newform subspaces 10
Sturm bound 3800
Trace bound 1

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Defining parameters

Level: \( N \) = \( 151 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 10 \)
Sturm bound: \(3800\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(151))\).

Total New Old
Modular forms 1025 1025 0
Cusp forms 876 876 0
Eisenstein series 149 149 0

Trace form

\( 876 q - 72 q^{2} - 71 q^{3} - 68 q^{4} - 69 q^{5} - 63 q^{6} - 67 q^{7} - 60 q^{8} - 62 q^{9} + O(q^{10}) \) \( 876 q - 72 q^{2} - 71 q^{3} - 68 q^{4} - 69 q^{5} - 63 q^{6} - 67 q^{7} - 60 q^{8} - 62 q^{9} - 57 q^{10} - 63 q^{11} - 47 q^{12} - 61 q^{13} - 51 q^{14} - 51 q^{15} - 44 q^{16} - 57 q^{17} - 36 q^{18} - 55 q^{19} - 33 q^{20} - 43 q^{21} - 39 q^{22} - 51 q^{23} - 15 q^{24} - 44 q^{25} - 33 q^{26} - 35 q^{27} - 19 q^{28} - 45 q^{29} - 3 q^{30} - 43 q^{31} - 12 q^{32} - 27 q^{33} - 21 q^{34} - 27 q^{35} + 16 q^{36} - 37 q^{37} - 15 q^{38} - 19 q^{39} + 15 q^{40} - 33 q^{41} + 21 q^{42} - 31 q^{43} + 9 q^{44} + 3 q^{45} - 3 q^{46} - 27 q^{47} + 49 q^{48} - 18 q^{49} + 18 q^{50} - 3 q^{51} + 23 q^{52} - 21 q^{53} + 45 q^{54} - 3 q^{55} + 45 q^{56} + 5 q^{57} + 15 q^{58} - 15 q^{59} + 93 q^{60} - 13 q^{61} + 21 q^{62} + 29 q^{63} + 52 q^{64} + 9 q^{65} + 69 q^{66} - 7 q^{67} + 51 q^{68} + 21 q^{69} + 69 q^{70} - 3 q^{71} + 120 q^{72} - q^{73} + 39 q^{74} + 49 q^{75} + 65 q^{76} + 21 q^{77} + 93 q^{78} + 5 q^{79} + 111 q^{80} + 46 q^{81} + 51 q^{82} + 9 q^{83} + 149 q^{84} + 33 q^{85} + 57 q^{86} + 45 q^{87} + 105 q^{88} + 15 q^{89} + 159 q^{90} + 37 q^{91} + 93 q^{92} + 53 q^{93} + 69 q^{94} + 45 q^{95} + 177 q^{96} + 23 q^{97} + 96 q^{98} + 81 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(151))\)

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
151.2.a \(\chi_{151}(1, \cdot)\) 151.2.a.a 3 1
151.2.a.b 3
151.2.a.c 6
151.2.c \(\chi_{151}(32, \cdot)\) 151.2.c.a 12 2
151.2.c.b 12
151.2.d \(\chi_{151}(8, \cdot)\) 151.2.d.a 12 4
151.2.d.b 32
151.2.g \(\chi_{151}(2, \cdot)\) 151.2.g.a 96 8
151.2.h \(\chi_{151}(9, \cdot)\) 151.2.h.a 220 20
151.2.k \(\chi_{151}(5, \cdot)\) 151.2.k.a 480 40