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Properties

Label 547.3.b
Level $547$
Weight $3$
Character orbit 547.b
Rep. character $\chi_{547}(546,\cdot)$
Character field $\Q$
Dimension $91$
Newform subspaces $2$
Sturm bound $137$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 547 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 547.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 547 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(137\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(547, [\chi])\).

Total New Old
Modular forms 93 93 0
Cusp forms 91 91 0
Eisenstein series 2 2 0

Trace form

\( 91 q - 180 q^{4} - 279 q^{9} + O(q^{10}) \) \( 91 q - 180 q^{4} - 279 q^{9} - 4 q^{10} - 32 q^{11} + 26 q^{13} - 26 q^{14} + 22 q^{15} + 284 q^{16} - 12 q^{19} - 16 q^{21} - 2 q^{24} - 469 q^{25} - 96 q^{29} + 26 q^{34} + 10 q^{35} + 472 q^{36} + 44 q^{40} + 124 q^{44} - 288 q^{46} - 310 q^{47} - 547 q^{49} + 86 q^{51} - 316 q^{52} + 24 q^{53} - 266 q^{54} + 158 q^{56} - 80 q^{60} + 40 q^{62} - 460 q^{64} + 528 q^{66} + 28 q^{67} + 16 q^{69} + 94 q^{73} - 614 q^{74} - 28 q^{76} - 98 q^{78} + 1171 q^{81} - 772 q^{82} + 358 q^{84} + 74 q^{85} - 410 q^{86} - 214 q^{90} + 656 q^{93} - 724 q^{96} + 346 q^{97} + 50 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(547, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
547.3.b.a 547.b 547.b $3$ $14.905$ 3.3.14769.1 \(\Q(\sqrt{-547}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+4q^{4}+9q^{9}+(3\beta _{1}+2\beta _{2})q^{11}+(-4\beta _{1}+\cdots)q^{13}+\cdots\)
547.3.b.b 547.b 547.b $88$ $14.905$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$