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Properties

Label 104.2
Level 104
Weight 2
Dimension 165
Nonzero newspaces 10
Newform subspaces 19
Sturm bound 1344
Trace bound 2

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Defining parameters

Level: \( N \) = \( 104 = 2^{3} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 19 \)
Sturm bound: \(1344\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(104))\).

Total New Old
Modular forms 408 209 199
Cusp forms 265 165 100
Eisenstein series 143 44 99

Trace form

\( 165 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{6} - 12 q^{7} - 12 q^{8} - 24 q^{9} + O(q^{10}) \) \( 165 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{6} - 12 q^{7} - 12 q^{8} - 24 q^{9} - 12 q^{10} - 12 q^{11} - 12 q^{12} - 24 q^{14} - 12 q^{15} - 12 q^{16} - 27 q^{17} - 12 q^{18} - 24 q^{19} - 12 q^{20} - 24 q^{21} - 12 q^{22} - 24 q^{23} - 12 q^{24} - 39 q^{25} - 12 q^{26} - 60 q^{27} - 12 q^{28} - 15 q^{29} - 12 q^{30} - 24 q^{31} - 12 q^{32} - 48 q^{33} - 12 q^{34} - 24 q^{35} + 24 q^{36} - 3 q^{37} - 12 q^{38} + 24 q^{40} - 15 q^{41} + 60 q^{42} + 36 q^{43} + 48 q^{44} + 45 q^{45} + 108 q^{46} + 24 q^{47} + 84 q^{48} - 12 q^{49} + 96 q^{50} + 72 q^{51} + 96 q^{52} + 36 q^{53} + 96 q^{54} + 60 q^{55} + 96 q^{56} - 12 q^{57} + 84 q^{58} + 24 q^{59} + 108 q^{60} + 45 q^{61} + 48 q^{62} + 12 q^{63} + 60 q^{64} - 51 q^{65} + 24 q^{66} - 24 q^{67} - 12 q^{68} - 36 q^{69} + 48 q^{70} - 60 q^{71} - 12 q^{72} - 72 q^{73} - 12 q^{74} - 36 q^{75} - 12 q^{76} - 48 q^{77} - 12 q^{78} - 48 q^{79} - 12 q^{80} - 72 q^{81} - 12 q^{82} - 72 q^{83} - 96 q^{84} - 39 q^{85} - 60 q^{86} + 12 q^{87} - 72 q^{88} - 24 q^{89} - 168 q^{90} + 60 q^{91} - 96 q^{92} + 36 q^{93} - 108 q^{94} + 84 q^{95} - 228 q^{96} + 12 q^{97} - 120 q^{98} + 180 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)

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
104.2.a \(\chi_{104}(1, \cdot)\) 104.2.a.a 1 1
104.2.a.b 2
104.2.b \(\chi_{104}(53, \cdot)\) 104.2.b.a 2 1
104.2.b.b 4
104.2.b.c 6
104.2.e \(\chi_{104}(77, \cdot)\) 104.2.e.a 2 1
104.2.e.b 2
104.2.e.c 8
104.2.f \(\chi_{104}(25, \cdot)\) 104.2.f.a 4 1
104.2.i \(\chi_{104}(9, \cdot)\) 104.2.i.a 2 2
104.2.i.b 4
104.2.k \(\chi_{104}(31, \cdot)\) None 0 2
104.2.m \(\chi_{104}(83, \cdot)\) 104.2.m.a 4 2
104.2.m.b 20
104.2.o \(\chi_{104}(17, \cdot)\) 104.2.o.a 8 2
104.2.r \(\chi_{104}(29, \cdot)\) 104.2.r.a 24 2
104.2.s \(\chi_{104}(69, \cdot)\) 104.2.s.a 4 2
104.2.s.b 4
104.2.s.c 16
104.2.u \(\chi_{104}(11, \cdot)\) 104.2.u.a 48 4
104.2.w \(\chi_{104}(7, \cdot)\) None 0 4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(104))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(104)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 1}\)