Properties

Label 547.2.a
Level 547
Weight 2
Character orbit a
Rep. character \(\chi_{547}(1,\cdot)\)
Character field \(\Q\)
Dimension 45
Newforms 3
Sturm bound 91
Trace bound 1

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Defining parameters

Level: \( N \) = \( 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 547.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(91\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(547))\).

Total New Old
Modular forms 46 46 0
Cusp forms 45 45 0
Eisenstein series 1 1 0

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

\(547\)Dim.
\(+\)\(20\)
\(-\)\(25\)

Trace form

\( 45q - 2q^{2} - 2q^{3} + 44q^{4} + 2q^{5} - 6q^{6} - 2q^{7} - 12q^{8} + 41q^{9} + O(q^{10}) \) \( 45q - 2q^{2} - 2q^{3} + 44q^{4} + 2q^{5} - 6q^{6} - 2q^{7} - 12q^{8} + 41q^{9} - 2q^{10} + 2q^{11} - 10q^{12} - 2q^{14} + 10q^{15} + 30q^{16} - 2q^{17} - 16q^{18} + 2q^{19} - 16q^{20} - 24q^{21} - 20q^{22} - 4q^{23} - 32q^{24} + 61q^{25} - 32q^{26} - 26q^{27} - 20q^{28} - 2q^{29} - 8q^{30} - 6q^{31} - 16q^{32} - 4q^{33} + 6q^{34} + 2q^{35} + 42q^{36} + 4q^{37} - 6q^{38} - 10q^{39} - 14q^{40} - 20q^{42} - 18q^{43} - 6q^{44} + 20q^{45} - 20q^{46} - 2q^{47} + 16q^{48} + 43q^{49} + 10q^{50} + 14q^{51} - 10q^{52} + 6q^{53} + 14q^{54} + 14q^{55} + 2q^{56} - 16q^{57} - 4q^{58} - 22q^{59} + 68q^{60} + 28q^{62} - 14q^{63} + 2q^{64} + 24q^{65} - 14q^{67} - 6q^{68} + 4q^{69} - 18q^{70} - 2q^{71} - 10q^{72} - 2q^{73} + 16q^{74} - 48q^{75} - 6q^{76} - 26q^{77} + 102q^{78} - 24q^{79} - 2q^{80} - 3q^{81} + 12q^{82} - 12q^{83} - 30q^{84} + 62q^{85} - 24q^{86} - 18q^{87} - 38q^{88} + 10q^{89} - 36q^{90} - 30q^{91} + 8q^{92} - 56q^{93} + 6q^{94} - 52q^{95} - 62q^{96} - 18q^{97} + 26q^{98} - 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(547))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 547
547.2.a.a \(2\) \(4.368\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(4\) \(+\) \(q+(-1+\beta )q^{2}-\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
547.2.a.b \(18\) \(4.368\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-4\) \(-10\) \(-27\) \(-11\) \(+\) \(q-\beta _{1}q^{2}+(-1+\beta _{9})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
547.2.a.c \(25\) \(4.368\) None \(4\) \(8\) \(29\) \(5\) \(-\)