Properties

Label 157.2
Level 157
Weight 2
Dimension 950
Nonzero newspaces 8
Newform subspaces 12
Sturm bound 4108
Trace bound 3

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 157 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 12 \)
Sturm bound: \(4108\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(157))\).

Total New Old
Modular forms 1105 1105 0
Cusp forms 950 950 0
Eisenstein series 155 155 0

Trace form

\( 950 q - 75 q^{2} - 74 q^{3} - 71 q^{4} - 72 q^{5} - 66 q^{6} - 70 q^{7} - 63 q^{8} - 65 q^{9} + O(q^{10}) \) \( 950 q - 75 q^{2} - 74 q^{3} - 71 q^{4} - 72 q^{5} - 66 q^{6} - 70 q^{7} - 63 q^{8} - 65 q^{9} - 60 q^{10} - 66 q^{11} - 50 q^{12} - 64 q^{13} - 54 q^{14} - 54 q^{15} - 47 q^{16} - 60 q^{17} - 39 q^{18} - 58 q^{19} - 36 q^{20} - 46 q^{21} - 42 q^{22} - 54 q^{23} - 18 q^{24} - 47 q^{25} - 36 q^{26} - 38 q^{27} - 22 q^{28} - 48 q^{29} - 6 q^{30} - 46 q^{31} - 15 q^{32} - 30 q^{33} - 24 q^{34} - 30 q^{35} + 13 q^{36} - 40 q^{37} - 18 q^{38} - 22 q^{39} + 12 q^{40} - 36 q^{41} + 18 q^{42} - 34 q^{43} + 6 q^{44} - 6 q^{46} - 30 q^{47} + 46 q^{48} - 21 q^{49} + 15 q^{50} - 6 q^{51} + 20 q^{52} - 24 q^{53} + 42 q^{54} - 6 q^{55} + 42 q^{56} + 2 q^{57} + 12 q^{58} - 18 q^{59} + 90 q^{60} - 16 q^{61} + 18 q^{62} + 26 q^{63} + 49 q^{64} + 6 q^{65} + 66 q^{66} - 10 q^{67} + 48 q^{68} + 18 q^{69} + 66 q^{70} - 6 q^{71} + 117 q^{72} - 4 q^{73} + 36 q^{74} + 46 q^{75} + 62 q^{76} + 18 q^{77} + 90 q^{78} + 2 q^{79} + 108 q^{80} + 43 q^{81} + 48 q^{82} + 6 q^{83} + 146 q^{84} + 30 q^{85} + 54 q^{86} + 42 q^{87} + 102 q^{88} + 12 q^{89} + 156 q^{90} + 34 q^{91} + 90 q^{92} + 50 q^{93} + 66 q^{94} + 42 q^{95} + 174 q^{96} + 20 q^{97} + 93 q^{98} + 78 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(157))\)

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
157.2.a \(\chi_{157}(1, \cdot)\) 157.2.a.a 5 1
157.2.a.b 7
157.2.b \(\chi_{157}(156, \cdot)\) 157.2.b.a 2 1
157.2.b.b 10
157.2.c \(\chi_{157}(12, \cdot)\) 157.2.c.a 24 2
157.2.e \(\chi_{157}(13, \cdot)\) 157.2.e.a 2 2
157.2.e.b 4
157.2.e.c 20
157.2.g \(\chi_{157}(14, \cdot)\) 157.2.g.a 132 12
157.2.h \(\chi_{157}(4, \cdot)\) 157.2.h.a 144 12
157.2.i \(\chi_{157}(9, \cdot)\) 157.2.i.a 288 24
157.2.k \(\chi_{157}(3, \cdot)\) 157.2.k.a 312 24