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Properties

Label 16.10
Level 16
Weight 10
Dimension 38
Nonzero newspaces 2
Newform subspaces 5
Sturm bound 160
Trace bound 1

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 5 \)
Sturm bound: \(160\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(16))\).

Total New Old
Modular forms 79 43 36
Cusp forms 65 38 27
Eisenstein series 14 5 9

Trace form

\( 38 q - 2 q^{2} - 82 q^{3} + 168 q^{4} - 362 q^{5} - 2192 q^{6} + 1376 q^{7} - 716 q^{8} + 5812 q^{9} + O(q^{10}) \) \( 38 q - 2 q^{2} - 82 q^{3} + 168 q^{4} - 362 q^{5} - 2192 q^{6} + 1376 q^{7} - 716 q^{8} + 5812 q^{9} + 4684 q^{10} + 54866 q^{11} + 217156 q^{12} - 43082 q^{13} - 133540 q^{14} + 465444 q^{15} - 817256 q^{16} + 172100 q^{17} + 2179902 q^{18} - 777226 q^{19} - 3277988 q^{20} - 297404 q^{21} - 34300 q^{22} + 1349664 q^{23} + 1863856 q^{24} - 30468 q^{25} - 6347768 q^{26} + 1359320 q^{27} + 3629528 q^{28} + 1090494 q^{29} - 4677804 q^{30} + 2669424 q^{31} - 1655992 q^{32} - 3529028 q^{33} - 4528204 q^{34} - 4843588 q^{35} + 23564140 q^{36} + 194014 q^{37} - 14996352 q^{38} + 46429600 q^{39} - 11751288 q^{40} + 4797864 q^{41} + 105399160 q^{42} - 113679270 q^{43} - 94223356 q^{44} - 2980422 q^{45} + 15432396 q^{46} + 236966224 q^{47} + 7831528 q^{48} - 123398326 q^{49} - 6289530 q^{50} - 230029084 q^{51} - 28284428 q^{52} - 84936562 q^{53} + 105311008 q^{54} + 216893536 q^{55} + 26511256 q^{56} + 25903936 q^{57} - 178271784 q^{58} - 129693942 q^{59} + 229034112 q^{60} - 100201754 q^{61} - 136788944 q^{62} + 139645668 q^{63} - 349292928 q^{64} - 1982060 q^{65} + 192273844 q^{66} + 150405926 q^{67} - 285757488 q^{68} + 503835060 q^{69} + 606051200 q^{70} - 39174048 q^{71} + 882075684 q^{72} - 15735768 q^{73} + 123910860 q^{74} - 762559722 q^{75} - 453269100 q^{76} + 166043716 q^{77} - 1735024804 q^{78} + 1572253888 q^{79} - 700272856 q^{80} - 888479154 q^{81} - 674287584 q^{82} - 878397074 q^{83} + 1281919912 q^{84} + 703120756 q^{85} + 243980676 q^{86} - 1417283424 q^{87} + 1781147128 q^{88} + 573376104 q^{89} + 3084087192 q^{90} + 3740994884 q^{91} - 3131634504 q^{92} + 67748240 q^{93} - 2068460272 q^{94} - 7241383788 q^{95} - 3896483152 q^{96} - 728181884 q^{97} - 3100632102 q^{98} + 6522651982 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(16))\)

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
16.10.a \(\chi_{16}(1, \cdot)\) 16.10.a.a 1 1
16.10.a.b 1
16.10.a.c 1
16.10.a.d 1
16.10.b \(\chi_{16}(9, \cdot)\) None 0 1
16.10.e \(\chi_{16}(5, \cdot)\) 16.10.e.a 34 2

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(16))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(16)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)