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Properties

Label 208.2
Level 208
Weight 2
Dimension 698
Nonzero newspaces 14
Newform subspaces 34
Sturm bound 5376
Trace bound 5

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Defining parameters

Level: \( N \) = \( 208 = 2^{4} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 14 \)
Newform subspaces: \( 34 \)
Sturm bound: \(5376\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(208))\).

Total New Old
Modular forms 1512 796 716
Cusp forms 1177 698 479
Eisenstein series 335 98 237

Trace form

\( 698 q - 20 q^{2} - 14 q^{3} - 24 q^{4} - 26 q^{5} - 32 q^{6} - 18 q^{7} - 32 q^{8} - 6 q^{9} + O(q^{10}) \) \( 698 q - 20 q^{2} - 14 q^{3} - 24 q^{4} - 26 q^{5} - 32 q^{6} - 18 q^{7} - 32 q^{8} - 6 q^{9} - 24 q^{10} - 22 q^{11} - 16 q^{12} - 28 q^{13} - 40 q^{14} - 26 q^{15} - 8 q^{16} - 46 q^{17} - 28 q^{18} - 30 q^{19} - 32 q^{20} - 38 q^{21} - 24 q^{22} - 18 q^{23} - 24 q^{24} - 12 q^{25} - 28 q^{26} - 20 q^{27} - 40 q^{28} - 42 q^{29} - 16 q^{30} + 14 q^{31} - 40 q^{32} - 46 q^{33} - 32 q^{34} - 10 q^{35} - 16 q^{36} - 42 q^{37} - 30 q^{39} - 32 q^{40} - 30 q^{41} - 24 q^{42} - 86 q^{43} - 16 q^{44} - 94 q^{45} - 48 q^{46} - 86 q^{47} - 40 q^{48} - 114 q^{49} - 12 q^{50} - 92 q^{51} - 20 q^{52} - 88 q^{53} - 24 q^{54} - 90 q^{55} - 8 q^{56} - 54 q^{57} - 42 q^{59} - 24 q^{60} - 54 q^{61} - 56 q^{62} - 74 q^{63} - 24 q^{64} - 82 q^{65} - 56 q^{66} - 10 q^{67} - 24 q^{68} - 6 q^{69} - 40 q^{70} - 18 q^{71} - 32 q^{72} - 6 q^{73} - 24 q^{74} - 12 q^{75} - 48 q^{76} - 44 q^{77} - 20 q^{78} - 36 q^{79} - 40 q^{80} - 92 q^{81} - 24 q^{82} - 14 q^{83} + 160 q^{84} - 14 q^{85} + 72 q^{86} + 18 q^{87} + 80 q^{88} + 90 q^{89} + 296 q^{90} + 26 q^{91} + 144 q^{92} + 130 q^{93} + 200 q^{94} + 66 q^{95} + 440 q^{96} + 50 q^{97} + 204 q^{98} + 82 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)

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
208.2.a \(\chi_{208}(1, \cdot)\) 208.2.a.a 1 1
208.2.a.b 1
208.2.a.c 1
208.2.a.d 1
208.2.a.e 2
208.2.b \(\chi_{208}(105, \cdot)\) None 0 1
208.2.e \(\chi_{208}(25, \cdot)\) None 0 1
208.2.f \(\chi_{208}(129, \cdot)\) 208.2.f.a 2 1
208.2.f.b 4
208.2.i \(\chi_{208}(81, \cdot)\) 208.2.i.a 2 2
208.2.i.b 2
208.2.i.c 2
208.2.i.d 2
208.2.i.e 4
208.2.k \(\chi_{208}(31, \cdot)\) 208.2.k.a 2 2
208.2.k.b 12
208.2.l \(\chi_{208}(83, \cdot)\) 208.2.l.a 2 2
208.2.l.b 50
208.2.n \(\chi_{208}(53, \cdot)\) 208.2.n.a 48 2
208.2.p \(\chi_{208}(77, \cdot)\) 208.2.p.a 8 2
208.2.p.b 44
208.2.s \(\chi_{208}(99, \cdot)\) 208.2.s.a 2 2
208.2.s.b 50
208.2.u \(\chi_{208}(135, \cdot)\) None 0 2
208.2.w \(\chi_{208}(17, \cdot)\) 208.2.w.a 2 2
208.2.w.b 2
208.2.w.c 8
208.2.z \(\chi_{208}(9, \cdot)\) None 0 2
208.2.ba \(\chi_{208}(121, \cdot)\) None 0 2
208.2.bc \(\chi_{208}(7, \cdot)\) None 0 4
208.2.bf \(\chi_{208}(11, \cdot)\) 208.2.bf.a 104 4
208.2.bh \(\chi_{208}(69, \cdot)\) 208.2.bh.a 104 4
208.2.bj \(\chi_{208}(29, \cdot)\) 208.2.bj.a 104 4
208.2.bk \(\chi_{208}(115, \cdot)\) 208.2.bk.a 104 4
208.2.bm \(\chi_{208}(15, \cdot)\) 208.2.bm.a 4 4
208.2.bm.b 4
208.2.bm.c 4
208.2.bm.d 4
208.2.bm.e 4
208.2.bm.f 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(208))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(208)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 1}\)