↑

Properties

Label 404.1
Level 404
Weight 1
Dimension 32
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 10200
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 404 = 2^{2} \cdot 101 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(10200\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(404))\).

Total New Old
Modular forms 282 130 152
Cusp forms 32 32 0
Eisenstein series 250 98 152

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 30 0 2 0

Trace form

\( 32 q - q^{2} - 2 q^{3} + 5 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} - q^{8} + 3 q^{9} + O(q^{10}) \) \( 32 q - q^{2} - 2 q^{3} + 5 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} - q^{8} + 3 q^{9} - 2 q^{10} - 2 q^{11} - 4 q^{13} - 2 q^{14} - 2 q^{15} + 5 q^{16} - 4 q^{17} - q^{18} + 2 q^{19} - 4 q^{20} - 4 q^{21} - 2 q^{22} - 2 q^{24} + q^{25} - 2 q^{26} - 2 q^{29} - 4 q^{30} - 2 q^{31} - q^{32} - 4 q^{33} - 2 q^{34} + 2 q^{35} + 3 q^{36} - 4 q^{37} - 2 q^{39} - 2 q^{40} - 2 q^{41} - 8 q^{45} + 3 q^{49} - 3 q^{50} + 2 q^{51} - 4 q^{52} - 4 q^{53} - 4 q^{54} - 2 q^{55} - 2 q^{56} - 2 q^{57} - 2 q^{58} - 2 q^{59} - 2 q^{61} - 2 q^{63} + 5 q^{64} - 8 q^{65} + 2 q^{67} - 4 q^{68} - 2 q^{69} - 4 q^{70} + 2 q^{71} - q^{72} - 2 q^{73} - 2 q^{74} - 4 q^{77} - 4 q^{78} + 2 q^{79} - 4 q^{80} + 3 q^{81} + 23 q^{82} - 4 q^{84} - 8 q^{85} - 2 q^{88} - 4 q^{89} - 2 q^{90} + 2 q^{91} + 2 q^{93} + 2 q^{95} - 2 q^{96} - 8 q^{97} - q^{98} + 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(404))\)

We only show spaces with odd 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
404.1.b \(\chi_{404}(203, \cdot)\) None 0 1
404.1.d \(\chi_{404}(403, \cdot)\) 404.1.d.a 3 1
404.1.d.b 3
404.1.f \(\chi_{404}(293, \cdot)\) 404.1.f.a 2 2
404.1.h \(\chi_{404}(107, \cdot)\) None 0 4
404.1.j \(\chi_{404}(87, \cdot)\) 404.1.j.a 4 4
404.1.k \(\chi_{404}(41, \cdot)\) None 0 8
404.1.n \(\chi_{404}(23, \cdot)\) None 0 20
404.1.o \(\chi_{404}(19, \cdot)\) 404.1.o.a 20 20
404.1.q \(\chi_{404}(29, \cdot)\) None 0 40