Properties

Label 547.2.a
Level $547$
Weight $2$
Character orbit 547.a
Rep. character $\chi_{547}(1,\cdot)$
Character field $\Q$
Dimension $45$
Newform subspaces $3$
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: \(\Q\)
Newform subspaces: \( 3 \)
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 and the Fricke involution.

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

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(547))\) 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
547.2.a.a 547.a 1.a $2$ $4.368$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(4\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}-\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
547.2.a.b 547.a 1.a $18$ $4.368$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-4\) \(-10\) \(-27\) \(-11\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1+\beta _{9})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
547.2.a.c 547.a 1.a $25$ $4.368$ None \(4\) \(8\) \(29\) \(5\) $-$ $\mathrm{SU}(2)$