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Properties

Label 6.10.a
Level $6$
Weight $10$
Character orbit 6.a
Rep. character $\chi_{6}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $10$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 6 = 2 \cdot 3 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 6.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(6))\).

Total New Old
Modular forms 11 1 10
Cusp forms 7 1 6
Eisenstein series 4 0 4

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)FrickeDim
\(+\)\(-\)$-$\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(1\)

Trace form

\( q - 16 q^{2} + 81 q^{3} + 256 q^{4} + 2694 q^{5} - 1296 q^{6} - 3544 q^{7} - 4096 q^{8} + 6561 q^{9} + O(q^{10}) \) \( q - 16 q^{2} + 81 q^{3} + 256 q^{4} + 2694 q^{5} - 1296 q^{6} - 3544 q^{7} - 4096 q^{8} + 6561 q^{9} - 43104 q^{10} + 29580 q^{11} + 20736 q^{12} - 44818 q^{13} + 56704 q^{14} + 218214 q^{15} + 65536 q^{16} - 101934 q^{17} - 104976 q^{18} - 895084 q^{19} + 689664 q^{20} - 287064 q^{21} - 473280 q^{22} - 1113000 q^{23} - 331776 q^{24} + 5304511 q^{25} + 717088 q^{26} + 531441 q^{27} - 907264 q^{28} - 2357346 q^{29} - 3491424 q^{30} + 175808 q^{31} - 1048576 q^{32} + 2395980 q^{33} + 1630944 q^{34} - 9547536 q^{35} + 1679616 q^{36} - 2919418 q^{37} + 14321344 q^{38} - 3630258 q^{39} - 11034624 q^{40} + 26218794 q^{41} + 4593024 q^{42} - 18762964 q^{43} + 7572480 q^{44} + 17675334 q^{45} + 17808000 q^{46} - 20966160 q^{47} + 5308416 q^{48} - 27793671 q^{49} - 84872176 q^{50} - 8256654 q^{51} - 11473408 q^{52} + 57251574 q^{53} - 8503056 q^{54} + 79688520 q^{55} + 14516224 q^{56} - 72501804 q^{57} + 37717536 q^{58} + 33587580 q^{59} + 55862784 q^{60} + 82260830 q^{61} - 2812928 q^{62} - 23252184 q^{63} + 16777216 q^{64} - 120739692 q^{65} - 38335680 q^{66} - 188455804 q^{67} - 26095104 q^{68} - 90153000 q^{69} + 152760576 q^{70} + 80924040 q^{71} - 26873856 q^{72} - 236140918 q^{73} + 46710688 q^{74} + 429665391 q^{75} - 229141504 q^{76} - 104831520 q^{77} + 58084128 q^{78} + 526909808 q^{79} + 176553984 q^{80} + 43046721 q^{81} - 419500704 q^{82} + 18346452 q^{83} - 73488384 q^{84} - 274610196 q^{85} + 300207424 q^{86} - 190945026 q^{87} - 121159680 q^{88} + 690643098 q^{89} - 282805344 q^{90} + 158834992 q^{91} - 284928000 q^{92} + 14240448 q^{93} + 335458560 q^{94} - 2411356296 q^{95} - 84934656 q^{96} - 438251038 q^{97} + 444698736 q^{98} + 194074380 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(6))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
6.10.a.a 6.a 1.a $1$ $3.090$ \(\Q\) None \(-16\) \(81\) \(2694\) \(-3544\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{4}q^{2}+3^{4}q^{3}+2^{8}q^{4}+2694q^{5}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(6))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(6)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)