Properties

Label 241.2
Level 241
Weight 2
Dimension 2301
Nonzero newspaces 16
Newform subspaces 17
Sturm bound 9680
Trace bound 2

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 241 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Newform subspaces: \( 17 \)
Sturm bound: \(9680\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(241))\).

Total New Old
Modular forms 2540 2540 0
Cusp forms 2301 2301 0
Eisenstein series 239 239 0

Trace form

\( 2301 q - 117 q^{2} - 116 q^{3} - 113 q^{4} - 114 q^{5} - 108 q^{6} - 112 q^{7} - 105 q^{8} - 107 q^{9} + O(q^{10}) \) \( 2301 q - 117 q^{2} - 116 q^{3} - 113 q^{4} - 114 q^{5} - 108 q^{6} - 112 q^{7} - 105 q^{8} - 107 q^{9} - 102 q^{10} - 108 q^{11} - 92 q^{12} - 106 q^{13} - 96 q^{14} - 96 q^{15} - 89 q^{16} - 102 q^{17} - 81 q^{18} - 100 q^{19} - 78 q^{20} - 88 q^{21} - 84 q^{22} - 96 q^{23} - 60 q^{24} - 89 q^{25} - 78 q^{26} - 80 q^{27} - 64 q^{28} - 90 q^{29} - 48 q^{30} - 88 q^{31} - 57 q^{32} - 72 q^{33} - 66 q^{34} - 72 q^{35} - 29 q^{36} - 82 q^{37} - 60 q^{38} - 64 q^{39} - 30 q^{40} - 78 q^{41} - 24 q^{42} - 76 q^{43} - 36 q^{44} - 42 q^{45} - 48 q^{46} - 72 q^{47} + 4 q^{48} - 63 q^{49} - 27 q^{50} - 48 q^{51} - 22 q^{52} - 66 q^{53} - 48 q^{55} - 40 q^{57} - 30 q^{58} - 60 q^{59} + 48 q^{60} - 58 q^{61} - 24 q^{62} - 16 q^{63} + 7 q^{64} - 36 q^{65} + 24 q^{66} - 52 q^{67} + 6 q^{68} - 24 q^{69} + 24 q^{70} - 48 q^{71} + 75 q^{72} - 46 q^{73} - 6 q^{74} + 4 q^{75} + 20 q^{76} - 24 q^{77} + 48 q^{78} - 40 q^{79} + 66 q^{80} + q^{81} + 6 q^{82} - 36 q^{83} + 104 q^{84} - 12 q^{85} + 12 q^{86} + 60 q^{88} - 30 q^{89} + 114 q^{90} - 8 q^{91} + 48 q^{92} + 8 q^{93} + 24 q^{94} + 132 q^{96} - 22 q^{97} + 51 q^{98} + 36 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(241))\)

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
241.2.a \(\chi_{241}(1, \cdot)\) 241.2.a.a 7 1
241.2.a.b 12
241.2.b \(\chi_{241}(240, \cdot)\) 241.2.b.a 18 1
241.2.c \(\chi_{241}(15, \cdot)\) 241.2.c.a 38 2
241.2.d \(\chi_{241}(64, \cdot)\) 241.2.d.a 36 2
241.2.e \(\chi_{241}(87, \cdot)\) 241.2.e.a 72 4
241.2.f \(\chi_{241}(16, \cdot)\) 241.2.f.a 38 2
241.2.g \(\chi_{241}(8, \cdot)\) 241.2.g.a 76 4
241.2.h \(\chi_{241}(36, \cdot)\) 241.2.h.a 72 4
241.2.i \(\chi_{241}(4, \cdot)\) 241.2.i.a 76 4
241.2.j \(\chi_{241}(24, \cdot)\) 241.2.j.a 152 8
241.2.l \(\chi_{241}(6, \cdot)\) 241.2.l.a 144 8
241.2.m \(\chi_{241}(2, \cdot)\) 241.2.m.a 160 8
241.2.n \(\chi_{241}(10, \cdot)\) 241.2.n.a 152 8
241.2.o \(\chi_{241}(5, \cdot)\) 241.2.o.a 304 16
241.2.q \(\chi_{241}(9, \cdot)\) 241.2.q.a 304 16
241.2.s \(\chi_{241}(3, \cdot)\) 241.2.s.a 640 32