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Properties

Label 6.14.a
Level $6$
Weight $14$
Character orbit 6.a
Rep. character $\chi_{6}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $14$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 6 = 2 \cdot 3 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 6.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(14\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(6))\).

Total New Old
Modular forms 15 1 14
Cusp forms 11 1 10
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

\( q + 64 q^{2} - 729 q^{3} + 4096 q^{4} + 54654 q^{5} - 46656 q^{6} + 176336 q^{7} + 262144 q^{8} + 531441 q^{9} + O(q^{10}) \) \( q + 64 q^{2} - 729 q^{3} + 4096 q^{4} + 54654 q^{5} - 46656 q^{6} + 176336 q^{7} + 262144 q^{8} + 531441 q^{9} + 3497856 q^{10} + 6612420 q^{11} - 2985984 q^{12} - 24028978 q^{13} + 11285504 q^{14} - 39842766 q^{15} + 16777216 q^{16} - 154665054 q^{17} + 34012224 q^{18} + 190034876 q^{19} + 223862784 q^{20} - 128548944 q^{21} + 423194880 q^{22} - 352957800 q^{23} - 191102976 q^{24} + 1766356591 q^{25} - 1537854592 q^{26} - 387420489 q^{27} + 722272256 q^{28} - 2804086266 q^{29} - 2549937024 q^{30} + 2763661208 q^{31} + 1073741824 q^{32} - 4820454180 q^{33} - 9898563456 q^{34} + 9637467744 q^{35} + 2176782336 q^{36} + 20030257622 q^{37} + 12162232064 q^{38} + 17517124962 q^{39} + 14327218176 q^{40} - 39624547206 q^{41} - 8227132416 q^{42} - 81486174844 q^{43} + 27084472320 q^{44} + 29045376414 q^{45} - 22589299200 q^{46} - 34136017440 q^{47} - 12230590464 q^{48} - 65794625511 q^{49} + 113046821824 q^{50} + 112750824366 q^{51} - 98422693888 q^{52} - 21810829986 q^{53} - 24794911296 q^{54} + 361395202680 q^{55} + 46225424384 q^{56} - 138535424604 q^{57} - 179461521024 q^{58} + 229219661220 q^{59} - 163195969536 q^{60} + 9799736750 q^{61} + 176874317312 q^{62} + 93712180176 q^{63} + 68719476736 q^{64} - 1313279763612 q^{65} - 308509067520 q^{66} + 789042707996 q^{67} - 633508061184 q^{68} + 257306236200 q^{69} + 616797935616 q^{70} - 369504705240 q^{71} + 139314069504 q^{72} - 693077725078 q^{73} + 1281936487808 q^{74} - 1287673954839 q^{75} + 778382852096 q^{76} + 1166007693120 q^{77} + 1121095997568 q^{78} + 2231309995208 q^{79} + 916941963264 q^{80} + 282429536481 q^{81} - 2535971021184 q^{82} + 2084328707772 q^{83} - 526536474624 q^{84} - 8453063861316 q^{85} - 5215115190016 q^{86} + 2044178887914 q^{87} + 1733406228480 q^{88} + 2221961096538 q^{89} + 1858904090496 q^{90} - 4237173864608 q^{91} - 1445715148800 q^{92} - 2014709020632 q^{93} - 2184705116160 q^{94} + 10386166112904 q^{95} - 782757789696 q^{96} + 10268379896642 q^{97} - 4210856032704 q^{98} + 3514111097220 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(6))\) 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
6.14.a.a 6.a 1.a $1$ $6.434$ \(\Q\) None \(64\) \(-729\) \(54654\) \(176336\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{6}q^{2}-3^{6}q^{3}+2^{12}q^{4}+54654q^{5}+\cdots\)

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(6))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_0(6)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)