Properties

Label 208.10
Level 208
Weight 10
Dimension 6674
Nonzero newspaces 14
Sturm bound 26880
Trace bound 5

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Defining parameters

Level: \( N \) = \( 208 = 2^{4} \cdot 13 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 14 \)
Sturm bound: \(26880\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(208))\).

Total New Old
Modular forms 12264 6772 5492
Cusp forms 11928 6674 5254
Eisenstein series 336 98 238

Trace form

\( 6674 q - 20 q^{2} + 146 q^{3} - 360 q^{4} + 694 q^{5} + 4360 q^{6} - 2770 q^{7} + 1408 q^{8} - 11630 q^{9} + O(q^{10}) \) \( 6674 q - 20 q^{2} + 146 q^{3} - 360 q^{4} + 694 q^{5} + 4360 q^{6} - 2770 q^{7} + 1408 q^{8} - 11630 q^{9} - 9392 q^{10} - 109750 q^{11} - 434336 q^{12} + 43052 q^{13} + 267032 q^{14} - 930906 q^{15} + 1634488 q^{16} - 344254 q^{17} - 4359828 q^{18} + 1554434 q^{19} + 6555952 q^{20} + 594778 q^{21} + 68576 q^{22} - 2699346 q^{23} - 3727736 q^{24} + 60924 q^{25} + 6347744 q^{26} - 2718676 q^{27} - 7259080 q^{28} - 2181018 q^{29} + 9355584 q^{30} - 5338866 q^{31} + 3311960 q^{32} + 7058002 q^{33} + 9056384 q^{34} + 9687158 q^{35} - 47128304 q^{36} - 388058 q^{37} + 29992680 q^{38} - 103957438 q^{39} + 23502528 q^{40} + 13090002 q^{41} - 210798344 q^{42} + 34938378 q^{43} + 188446688 q^{44} + 147284754 q^{45} - 30864816 q^{46} - 310798934 q^{47} - 15663080 q^{48} + 169354118 q^{49} + 12579036 q^{50} - 27036316 q^{51} + 28284404 q^{52} + 45741560 q^{53} - 210622040 q^{54} + 96478438 q^{55} - 53022536 q^{56} + 422866378 q^{57} + 356543544 q^{58} + 149257206 q^{59} - 458068248 q^{60} - 880486982 q^{61} + 273577864 q^{62} - 440849418 q^{63} + 698585832 q^{64} + 864786782 q^{65} - 384547736 q^{66} - 1375020586 q^{67} + 571514952 q^{68} - 1007670150 q^{69} - 1212102424 q^{70} + 78348078 q^{71} - 1764151392 q^{72} + 31471530 q^{73} - 247821744 q^{74} + 1525237524 q^{75} + 906538176 q^{76} - 332087468 q^{77} + 1735024780 q^{78} - 3144507812 q^{79} + 1400545688 q^{80} + 1776840156 q^{81} + 1348575144 q^{82} + 1756794130 q^{83} - 1595353280 q^{84} + 3919284562 q^{85} - 7471037952 q^{86} - 1132827822 q^{87} - 9139514960 q^{88} + 1760912010 q^{89} + 18355821504 q^{90} + 438117850 q^{91} + 15151204272 q^{92} + 3089758082 q^{93} - 1958054392 q^{94} + 10263452418 q^{95} - 31072808392 q^{96} - 6907333598 q^{97} - 7482726564 q^{98} - 15380541518 q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(208))\)

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
208.10.a \(\chi_{208}(1, \cdot)\) 208.10.a.a 1 1
208.10.a.b 1
208.10.a.c 1
208.10.a.d 3
208.10.a.e 3
208.10.a.f 4
208.10.a.g 4
208.10.a.h 5
208.10.a.i 5
208.10.a.j 6
208.10.a.k 6
208.10.a.l 7
208.10.a.m 8
208.10.b \(\chi_{208}(105, \cdot)\) None 0 1
208.10.e \(\chi_{208}(25, \cdot)\) None 0 1
208.10.f \(\chi_{208}(129, \cdot)\) 208.10.f.a 10 1
208.10.f.b 10
208.10.f.c 10
208.10.f.d 32
208.10.i \(\chi_{208}(81, \cdot)\) n/a 124 2
208.10.k \(\chi_{208}(31, \cdot)\) n/a 126 2
208.10.l \(\chi_{208}(83, \cdot)\) n/a 500 2
208.10.n \(\chi_{208}(53, \cdot)\) n/a 432 2
208.10.p \(\chi_{208}(77, \cdot)\) n/a 500 2
208.10.s \(\chi_{208}(99, \cdot)\) n/a 500 2
208.10.u \(\chi_{208}(135, \cdot)\) None 0 2
208.10.w \(\chi_{208}(17, \cdot)\) n/a 124 2
208.10.z \(\chi_{208}(9, \cdot)\) None 0 2
208.10.ba \(\chi_{208}(121, \cdot)\) None 0 2
208.10.bc \(\chi_{208}(7, \cdot)\) None 0 4
208.10.bf \(\chi_{208}(11, \cdot)\) n/a 1000 4
208.10.bh \(\chi_{208}(69, \cdot)\) n/a 1000 4
208.10.bj \(\chi_{208}(29, \cdot)\) n/a 1000 4
208.10.bk \(\chi_{208}(115, \cdot)\) n/a 1000 4
208.10.bm \(\chi_{208}(15, \cdot)\) n/a 252 4

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

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(208))\) into lower level spaces

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