Properties

Label 208.6
Level 208
Weight 6
Dimension 3686
Nonzero newspaces 14
Sturm bound 16128
Trace bound 5

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Defining parameters

Level: \( N \) = \( 208 = 2^{4} \cdot 13 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 14 \)
Sturm bound: \(16128\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(208))\).

Total New Old
Modular forms 6888 3784 3104
Cusp forms 6552 3686 2866
Eisenstein series 336 98 238

Trace form

\( 3686 q - 20 q^{2} + 2 q^{3} + 24 q^{4} + 14 q^{5} - 248 q^{6} - 242 q^{7} - 512 q^{8} - 122 q^{9} + O(q^{10}) \) \( 3686 q - 20 q^{2} + 2 q^{3} + 24 q^{4} + 14 q^{5} - 248 q^{6} - 242 q^{7} - 512 q^{8} - 122 q^{9} + 848 q^{10} + 2522 q^{11} - 32 q^{12} - 88 q^{13} + 152 q^{14} - 7866 q^{15} + 1720 q^{16} + 1162 q^{17} + 6252 q^{18} + 12466 q^{19} - 5968 q^{20} - 2150 q^{21} - 8864 q^{22} - 7858 q^{23} - 16760 q^{24} - 4296 q^{25} - 7392 q^{26} - 3700 q^{27} + 14648 q^{28} - 418 q^{29} + 60864 q^{30} + 20110 q^{31} + 47960 q^{32} + 7954 q^{33} + 3456 q^{34} - 23242 q^{35} - 13808 q^{36} + 1214 q^{37} - 106520 q^{38} - 50350 q^{39} - 150592 q^{40} - 1830 q^{41} - 66824 q^{42} + 99098 q^{43} + 80224 q^{44} + 114714 q^{45} + 185040 q^{46} - 51158 q^{47} + 295960 q^{48} - 8438 q^{49} + 170076 q^{50} - 243964 q^{51} - 91596 q^{52} - 216944 q^{53} - 417368 q^{54} - 6202 q^{55} - 382280 q^{56} - 24374 q^{57} - 213576 q^{58} + 212902 q^{59} + 308712 q^{60} + 477314 q^{61} + 547720 q^{62} + 154710 q^{63} + 567528 q^{64} - 75898 q^{65} + 306664 q^{66} - 59866 q^{67} - 267448 q^{68} - 151494 q^{69} - 824344 q^{70} - 157682 q^{71} - 940512 q^{72} - 125358 q^{73} - 294320 q^{74} - 208956 q^{75} + 174912 q^{76} + 18836 q^{77} + 631756 q^{78} + 40988 q^{79} + 1108888 q^{80} + 220224 q^{81} + 186408 q^{82} - 185534 q^{83} + 21568 q^{84} + 745762 q^{85} + 629120 q^{86} + 109362 q^{87} - 1304400 q^{88} - 779022 q^{89} - 3358656 q^{90} - 237702 q^{91} - 1038160 q^{92} - 1806334 q^{93} - 507640 q^{94} - 166622 q^{95} + 116792 q^{96} + 169002 q^{97} + 1511132 q^{98} + 1034818 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(208))\)

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
208.6.a \(\chi_{208}(1, \cdot)\) 208.6.a.a 1 1
208.6.a.b 1
208.6.a.c 1
208.6.a.d 1
208.6.a.e 2
208.6.a.f 2
208.6.a.g 2
208.6.a.h 2
208.6.a.i 3
208.6.a.j 3
208.6.a.k 3
208.6.a.l 4
208.6.a.m 5
208.6.b \(\chi_{208}(105, \cdot)\) None 0 1
208.6.e \(\chi_{208}(25, \cdot)\) None 0 1
208.6.f \(\chi_{208}(129, \cdot)\) 208.6.f.a 2 1
208.6.f.b 2
208.6.f.c 6
208.6.f.d 6
208.6.f.e 18
208.6.i \(\chi_{208}(81, \cdot)\) 208.6.i.a 6 2
208.6.i.b 8
208.6.i.c 8
208.6.i.d 12
208.6.i.e 16
208.6.i.f 18
208.6.k \(\chi_{208}(31, \cdot)\) 208.6.k.a 2 2
208.6.k.b 24
208.6.k.c 44
208.6.l \(\chi_{208}(83, \cdot)\) n/a 276 2
208.6.n \(\chi_{208}(53, \cdot)\) n/a 240 2
208.6.p \(\chi_{208}(77, \cdot)\) n/a 276 2
208.6.s \(\chi_{208}(99, \cdot)\) n/a 276 2
208.6.u \(\chi_{208}(135, \cdot)\) None 0 2
208.6.w \(\chi_{208}(17, \cdot)\) 208.6.w.a 10 2
208.6.w.b 10
208.6.w.c 12
208.6.w.d 36
208.6.z \(\chi_{208}(9, \cdot)\) None 0 2
208.6.ba \(\chi_{208}(121, \cdot)\) None 0 2
208.6.bc \(\chi_{208}(7, \cdot)\) None 0 4
208.6.bf \(\chi_{208}(11, \cdot)\) n/a 552 4
208.6.bh \(\chi_{208}(69, \cdot)\) n/a 552 4
208.6.bj \(\chi_{208}(29, \cdot)\) n/a 552 4
208.6.bk \(\chi_{208}(115, \cdot)\) n/a 552 4
208.6.bm \(\chi_{208}(15, \cdot)\) n/a 140 4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(208))\) into lower level spaces

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