Properties

Label 6.4.a
Level $6$
Weight $4$
Character orbit 6.a
Rep. character $\chi_{6}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $4$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 6 = 2 \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 6.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(6))\).

Total New Old
Modular forms 5 1 4
Cusp forms 1 1 0
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\(+\)\(1\)
Minus space\(-\)\(0\)

Trace form

\( q - 2 q^{2} - 3 q^{3} + 4 q^{4} + 6 q^{5} + 6 q^{6} - 16 q^{7} - 8 q^{8} + 9 q^{9} + O(q^{10}) \) \( q - 2 q^{2} - 3 q^{3} + 4 q^{4} + 6 q^{5} + 6 q^{6} - 16 q^{7} - 8 q^{8} + 9 q^{9} - 12 q^{10} + 12 q^{11} - 12 q^{12} + 38 q^{13} + 32 q^{14} - 18 q^{15} + 16 q^{16} - 126 q^{17} - 18 q^{18} + 20 q^{19} + 24 q^{20} + 48 q^{21} - 24 q^{22} + 168 q^{23} + 24 q^{24} - 89 q^{25} - 76 q^{26} - 27 q^{27} - 64 q^{28} + 30 q^{29} + 36 q^{30} - 88 q^{31} - 32 q^{32} - 36 q^{33} + 252 q^{34} - 96 q^{35} + 36 q^{36} + 254 q^{37} - 40 q^{38} - 114 q^{39} - 48 q^{40} + 42 q^{41} - 96 q^{42} - 52 q^{43} + 48 q^{44} + 54 q^{45} - 336 q^{46} - 96 q^{47} - 48 q^{48} - 87 q^{49} + 178 q^{50} + 378 q^{51} + 152 q^{52} + 198 q^{53} + 54 q^{54} + 72 q^{55} + 128 q^{56} - 60 q^{57} - 60 q^{58} - 660 q^{59} - 72 q^{60} - 538 q^{61} + 176 q^{62} - 144 q^{63} + 64 q^{64} + 228 q^{65} + 72 q^{66} + 884 q^{67} - 504 q^{68} - 504 q^{69} + 192 q^{70} + 792 q^{71} - 72 q^{72} + 218 q^{73} - 508 q^{74} + 267 q^{75} + 80 q^{76} - 192 q^{77} + 228 q^{78} - 520 q^{79} + 96 q^{80} + 81 q^{81} - 84 q^{82} - 492 q^{83} + 192 q^{84} - 756 q^{85} + 104 q^{86} - 90 q^{87} - 96 q^{88} + 810 q^{89} - 108 q^{90} - 608 q^{91} + 672 q^{92} + 264 q^{93} + 192 q^{94} + 120 q^{95} + 96 q^{96} + 1154 q^{97} + 174 q^{98} + 108 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\) 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
6.4.a.a 6.a 1.a $1$ $0.354$ \(\Q\) None \(-2\) \(-3\) \(6\) \(-16\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+6q^{5}+6q^{6}+\cdots\)