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Properties

Label 547.6.a
Level $547$
Weight $6$
Character orbit 547.a
Rep. character $\chi_{547}(1,\cdot)$
Character field $\Q$
Dimension $228$
Newform subspaces $2$
Sturm bound $274$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 547 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 547.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(274\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(547))\).

Total New Old
Modular forms 230 228 2
Cusp forms 228 228 0
Eisenstein series 2 0 2

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

\(547\)Dim
\(+\)\(111\)
\(-\)\(117\)

Trace form

\( 228 q - 4 q^{2} + 2 q^{3} + 3684 q^{4} - 52 q^{5} - 108 q^{6} - 194 q^{7} - 192 q^{8} + 18912 q^{9} + O(q^{10}) \) \( 228 q - 4 q^{2} + 2 q^{3} + 3684 q^{4} - 52 q^{5} - 108 q^{6} - 194 q^{7} - 192 q^{8} + 18912 q^{9} - 100 q^{10} - 34 q^{11} + 1218 q^{12} + 50 q^{13} - 930 q^{14} - 1574 q^{15} + 60996 q^{16} + 1604 q^{17} - 7902 q^{18} - 4394 q^{19} - 2464 q^{20} + 784 q^{21} + 928 q^{22} - 5964 q^{23} - 2594 q^{24} + 142374 q^{25} + 3896 q^{26} - 2386 q^{27} + 16 q^{28} + 9868 q^{29} + 11164 q^{30} - 654 q^{31} + 5032 q^{32} + 36 q^{33} + 24890 q^{34} + 21634 q^{35} + 337288 q^{36} - 5430 q^{37} - 15014 q^{38} + 8518 q^{39} - 45664 q^{40} - 7502 q^{41} + 9672 q^{42} + 458 q^{43} - 17184 q^{44} - 5110 q^{45} + 32076 q^{46} + 66382 q^{47} + 7044 q^{48} + 517950 q^{49} + 20708 q^{50} - 17306 q^{51} - 9156 q^{52} + 10524 q^{53} + 242 q^{54} + 19758 q^{55} - 66862 q^{56} + 69560 q^{57} + 20944 q^{58} + 38 q^{59} - 29900 q^{60} - 60474 q^{61} - 79372 q^{62} - 102542 q^{63} + 977652 q^{64} - 73748 q^{65} - 96600 q^{66} + 42438 q^{67} + 112114 q^{68} - 181524 q^{69} - 134114 q^{70} - 109378 q^{71} - 449362 q^{72} + 57084 q^{73} + 36146 q^{74} + 130956 q^{75} - 131448 q^{76} + 15562 q^{77} - 224302 q^{78} + 9784 q^{79} - 126182 q^{80} + 1433596 q^{81} + 223516 q^{82} - 131080 q^{83} - 96098 q^{84} - 25106 q^{85} - 41954 q^{86} - 177042 q^{87} - 341522 q^{88} - 245872 q^{89} - 645358 q^{90} + 22434 q^{91} - 703996 q^{92} + 12464 q^{93} + 340754 q^{94} + 130372 q^{95} - 341916 q^{96} + 412268 q^{97} - 200176 q^{98} - 212788 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(547))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 547
547.6.a.a 547.a 1.a $111$ $87.730$ None \(-28\) \(-98\) \(-801\) \(-587\) $+$ $\mathrm{SU}(2)$
547.6.a.b 547.a 1.a $117$ $87.730$ None \(24\) \(100\) \(749\) \(393\) $-$ $\mathrm{SU}(2)$