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Properties

Label 1.16.a
Level $1$
Weight $16$
Character orbit 1.a
Rep. character $\chi_{1}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $1$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 16 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(1\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_0(1))\).

Total New Old
Modular forms 2 2 0
Cusp forms 1 1 0
Eisenstein series 1 1 0

Trace form

\( q + 216 q^{2} - 3348 q^{3} + 13888 q^{4} + 52110 q^{5} - 723168 q^{6} + 2822456 q^{7} - 4078080 q^{8} - 3139803 q^{9} + O(q^{10}) \) \( q + 216 q^{2} - 3348 q^{3} + 13888 q^{4} + 52110 q^{5} - 723168 q^{6} + 2822456 q^{7} - 4078080 q^{8} - 3139803 q^{9} + 11255760 q^{10} + 20586852 q^{11} - 46497024 q^{12} - 190073338 q^{13} + 609650496 q^{14} - 174464280 q^{15} - 1335947264 q^{16} + 1646527986 q^{17} - 678197448 q^{18} + 1563257180 q^{19} + 723703680 q^{20} - 9449582688 q^{21} + 4446760032 q^{22} + 9451116072 q^{23} + 13653411840 q^{24} - 27802126025 q^{25} - 41055841008 q^{26} + 58552201080 q^{27} + 39198268928 q^{28} - 36902568330 q^{29} - 37684284480 q^{30} + 71588483552 q^{31} - 154934083584 q^{32} - 68924780496 q^{33} + 355650044976 q^{34} + 147078182160 q^{35} - 43605584064 q^{36} - 1033652081554 q^{37} + 337663550880 q^{38} + 636365535624 q^{39} - 212508748800 q^{40} + 1641974018202 q^{41} - 2041109860608 q^{42} - 492403109308 q^{43} + 285910200576 q^{44} - 163615134330 q^{45} + 2041441071552 q^{46} - 3410684952624 q^{47} + 4472751439872 q^{48} + 3218696361993 q^{49} - 6005259221400 q^{50} - 5512575697128 q^{51} - 2639738518144 q^{52} + 6797151655902 q^{53} + 12647275433280 q^{54} + 1072780857720 q^{55} - 11510201364480 q^{56} - 5233785038640 q^{57} - 7970954759280 q^{58} + 9858856815540 q^{59} - 2422959920640 q^{60} + 4931842626902 q^{61} + 15463112447232 q^{62} - 8861955816168 q^{63} + 10310557892608 q^{64} - 9904721643180 q^{65} - 14887752587136 q^{66} - 28837826625364 q^{67} + 22866980669568 q^{68} - 31642336609056 q^{69} + 31768887346560 q^{70} + 125050114914552 q^{71} + 12804367818240 q^{72} - 82171455513478 q^{73} - 223268849615664 q^{74} + 93081517931700 q^{75} + 21710515715840 q^{76} + 58105483948512 q^{77} + 137454955694784 q^{78} - 25413078694480 q^{79} - 69616211927040 q^{80} - 150980027970519 q^{81} + 354666387931632 q^{82} - 281736730890468 q^{83} - 131235804370944 q^{84} + 85800573350460 q^{85} - 106359071610528 q^{86} + 123549798768840 q^{87} - 83954829404160 q^{88} + 715618564776810 q^{89} - 35340869015280 q^{90} - 536473633278128 q^{91} + 131257100007936 q^{92} - 239678242932096 q^{93} - 736707949766784 q^{94} + 81461331649800 q^{95} + 518719311839232 q^{96} + 612786136081826 q^{97} + 695238414190488 q^{98} - 64638659670156 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_0(1))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1.16.a.a 1.a 1.a $1$ $1.427$ \(\Q\) None \(216\) \(-3348\) \(52110\) \(2822456\) $+$ $\mathrm{SU}(2)$ \(q+6^{3}q^{2}-3348q^{3}+13888q^{4}+52110q^{5}+\cdots\)