↑

Properties

Label 401.2
Level 401
Weight 2
Dimension 6501
Nonzero newspaces 12
Newform subspaces 15
Sturm bound 26800
Trace bound 2

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 401 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 15 \)
Sturm bound: \(26800\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(401))\).

Total New Old
Modular forms 6900 6900 0
Cusp forms 6501 6501 0
Eisenstein series 399 399 0

Trace form

\( 6501 q - 197 q^{2} - 196 q^{3} - 193 q^{4} - 194 q^{5} - 188 q^{6} - 192 q^{7} - 185 q^{8} - 187 q^{9} + O(q^{10}) \) \( 6501 q - 197 q^{2} - 196 q^{3} - 193 q^{4} - 194 q^{5} - 188 q^{6} - 192 q^{7} - 185 q^{8} - 187 q^{9} - 182 q^{10} - 188 q^{11} - 172 q^{12} - 186 q^{13} - 176 q^{14} - 176 q^{15} - 169 q^{16} - 182 q^{17} - 161 q^{18} - 180 q^{19} - 158 q^{20} - 168 q^{21} - 164 q^{22} - 176 q^{23} - 140 q^{24} - 169 q^{25} - 158 q^{26} - 160 q^{27} - 144 q^{28} - 170 q^{29} - 128 q^{30} - 168 q^{31} - 137 q^{32} - 152 q^{33} - 146 q^{34} - 152 q^{35} - 109 q^{36} - 162 q^{37} - 140 q^{38} - 144 q^{39} - 110 q^{40} - 158 q^{41} - 104 q^{42} - 156 q^{43} - 116 q^{44} - 122 q^{45} - 128 q^{46} - 152 q^{47} - 76 q^{48} - 143 q^{49} - 107 q^{50} - 128 q^{51} - 102 q^{52} - 146 q^{53} - 80 q^{54} - 128 q^{55} - 80 q^{56} - 120 q^{57} - 110 q^{58} - 140 q^{59} - 32 q^{60} - 138 q^{61} - 104 q^{62} - 96 q^{63} - 73 q^{64} - 116 q^{65} - 56 q^{66} - 132 q^{67} - 74 q^{68} - 104 q^{69} - 56 q^{70} - 128 q^{71} - 5 q^{72} - 126 q^{73} - 86 q^{74} - 76 q^{75} - 60 q^{76} - 104 q^{77} - 32 q^{78} - 120 q^{79} - 14 q^{80} - 79 q^{81} - 74 q^{82} - 116 q^{83} + 24 q^{84} - 92 q^{85} - 68 q^{86} - 80 q^{87} - 20 q^{88} - 110 q^{89} + 34 q^{90} - 88 q^{91} - 32 q^{92} - 72 q^{93} - 56 q^{94} - 80 q^{95} + 52 q^{96} - 102 q^{97} - 29 q^{98} - 44 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(401))\)

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
401.2.a \(\chi_{401}(1, \cdot)\) 401.2.a.a 12 1
401.2.a.b 21
401.2.b \(\chi_{401}(400, \cdot)\) 401.2.b.a 32 1
401.2.c \(\chi_{401}(20, \cdot)\) 401.2.c.a 64 2
401.2.d \(\chi_{401}(39, \cdot)\) 401.2.d.a 4 4
401.2.d.b 124
401.2.e \(\chi_{401}(45, \cdot)\) 401.2.e.a 4 4
401.2.e.b 128
401.2.f \(\chi_{401}(29, \cdot)\) 401.2.f.a 128 4
401.2.h \(\chi_{401}(22, \cdot)\) 401.2.h.a 256 8
401.2.i \(\chi_{401}(5, \cdot)\) 401.2.i.a 640 20
401.2.j \(\chi_{401}(32, \cdot)\) 401.2.j.a 528 16
401.2.k \(\chi_{401}(14, \cdot)\) 401.2.k.a 640 20
401.2.m \(\chi_{401}(4, \cdot)\) 401.2.m.a 1280 40
401.2.n \(\chi_{401}(2, \cdot)\) 401.2.n.a 2640 80