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Properties

Label 547.8.a
Level $547$
Weight $8$
Character orbit 547.a
Rep. character $\chi_{547}(1,\cdot)$
Character field $\Q$
Dimension $318$
Newform subspaces $2$
Sturm bound $365$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 547 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 547.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(365\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(547))\).

Total New Old
Modular forms 320 318 2
Cusp forms 318 318 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
\(+\)\(162\)
\(-\)\(156\)

Trace form

\( 318 q - 8 q^{2} + 26 q^{3} + 20340 q^{4} + 248 q^{5} - 324 q^{6} + 1742 q^{7} - 1536 q^{8} + 227058 q^{9} + O(q^{10}) \) \( 318 q - 8 q^{2} + 26 q^{3} + 20340 q^{4} + 248 q^{5} - 324 q^{6} + 1742 q^{7} - 1536 q^{8} + 227058 q^{9} - 3140 q^{10} - 250 q^{11} - 2574 q^{12} - 11798 q^{13} + 30622 q^{14} + 8218 q^{15} + 1283844 q^{16} + 26512 q^{17} + 42894 q^{18} + 37262 q^{19} + 20864 q^{20} - 93296 q^{21} - 66688 q^{22} + 169460 q^{23} - 177698 q^{24} + 4808832 q^{25} - 42128 q^{26} - 187642 q^{27} + 81488 q^{28} - 307448 q^{29} - 476948 q^{30} - 137742 q^{31} - 825496 q^{32} + 485772 q^{33} + 403810 q^{34} - 736918 q^{35} + 14051512 q^{36} + 96354 q^{37} + 1404042 q^{38} - 51098 q^{39} + 1580704 q^{40} - 483390 q^{41} + 616392 q^{42} - 174542 q^{43} + 1037520 q^{44} + 1965122 q^{45} - 311508 q^{46} - 1402418 q^{47} + 1116180 q^{48} + 36543396 q^{49} - 3391304 q^{50} + 2193454 q^{51} - 552564 q^{52} + 3416280 q^{53} - 1099726 q^{54} + 1225662 q^{55} + 6528002 q^{56} - 4027672 q^{57} - 902632 q^{58} + 508046 q^{59} + 4834996 q^{60} + 672822 q^{61} + 3575188 q^{62} + 6049090 q^{63} + 80711316 q^{64} + 1695660 q^{65} + 5309976 q^{66} - 4083282 q^{67} + 10516530 q^{68} + 9025332 q^{69} + 5137646 q^{70} - 1552802 q^{71} + 636110 q^{72} - 3130584 q^{73} - 6270830 q^{74} + 2902092 q^{75} - 7253784 q^{76} + 5607790 q^{77} + 4877570 q^{78} - 1319272 q^{79} + 4440922 q^{80} + 171143398 q^{81} - 85084 q^{82} - 4850424 q^{83} - 19625426 q^{84} + 1943282 q^{85} + 834342 q^{86} - 1356306 q^{87} - 8111794 q^{88} - 14897228 q^{89} + 26654642 q^{90} + 3933930 q^{91} + 29149652 q^{92} - 14036224 q^{93} + 44200450 q^{94} + 7475156 q^{95} - 40931532 q^{96} - 10310120 q^{97} - 35789524 q^{98} + 437756 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(547))\) 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
547.8.a.a 547.a 1.a $156$ $170.875$ None \(-56\) \(-284\) \(-3751\) \(-2559\) $-$ $\mathrm{SU}(2)$
547.8.a.b 547.a 1.a $162$ $170.875$ None \(48\) \(310\) \(3999\) \(4301\) $+$ $\mathrm{SU}(2)$