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Properties

Label 6.6.a
Level $6$
Weight $6$
Character orbit 6.a
Rep. character $\chi_{6}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $6$
Trace bound $0$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 7 1 6
Cusp forms 3 1 2
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

\( q + 4 q^{2} - 9 q^{3} + 16 q^{4} - 66 q^{5} - 36 q^{6} + 176 q^{7} + 64 q^{8} + 81 q^{9} + O(q^{10}) \) \( q + 4 q^{2} - 9 q^{3} + 16 q^{4} - 66 q^{5} - 36 q^{6} + 176 q^{7} + 64 q^{8} + 81 q^{9} - 264 q^{10} - 60 q^{11} - 144 q^{12} - 658 q^{13} + 704 q^{14} + 594 q^{15} + 256 q^{16} - 414 q^{17} + 324 q^{18} + 956 q^{19} - 1056 q^{20} - 1584 q^{21} - 240 q^{22} + 600 q^{23} - 576 q^{24} + 1231 q^{25} - 2632 q^{26} - 729 q^{27} + 2816 q^{28} + 5574 q^{29} + 2376 q^{30} - 3592 q^{31} + 1024 q^{32} + 540 q^{33} - 1656 q^{34} - 11616 q^{35} + 1296 q^{36} - 8458 q^{37} + 3824 q^{38} + 5922 q^{39} - 4224 q^{40} + 19194 q^{41} - 6336 q^{42} + 13316 q^{43} - 960 q^{44} - 5346 q^{45} + 2400 q^{46} - 19680 q^{47} - 2304 q^{48} + 14169 q^{49} + 4924 q^{50} + 3726 q^{51} - 10528 q^{52} - 31266 q^{53} - 2916 q^{54} + 3960 q^{55} + 11264 q^{56} - 8604 q^{57} + 22296 q^{58} + 26340 q^{59} + 9504 q^{60} - 31090 q^{61} - 14368 q^{62} + 14256 q^{63} + 4096 q^{64} + 43428 q^{65} + 2160 q^{66} - 16804 q^{67} - 6624 q^{68} - 5400 q^{69} - 46464 q^{70} + 6120 q^{71} + 5184 q^{72} - 25558 q^{73} - 33832 q^{74} - 11079 q^{75} + 15296 q^{76} - 10560 q^{77} + 23688 q^{78} + 74408 q^{79} - 16896 q^{80} + 6561 q^{81} + 76776 q^{82} - 6468 q^{83} - 25344 q^{84} + 27324 q^{85} + 53264 q^{86} - 50166 q^{87} - 3840 q^{88} - 32742 q^{89} - 21384 q^{90} - 115808 q^{91} + 9600 q^{92} + 32328 q^{93} - 78720 q^{94} - 63096 q^{95} - 9216 q^{96} + 166082 q^{97} + 56676 q^{98} - 4860 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(6))\) 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
6.6.a.a 6.a 1.a $1$ $0.962$ \(\Q\) None \(4\) \(-9\) \(-66\) \(176\) $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{2}-9q^{3}+2^{4}q^{4}-66q^{5}-6^{2}q^{6}+\cdots\)

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

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