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Properties

Label 273.2.bf
Level $273$
Weight $2$
Character orbit 273.bf
Rep. character $\chi_{273}(152,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $66$
Newform subspaces $2$
Sturm bound $74$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(74\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(273, [\chi])\).

Total New Old
Modular forms 82 82 0
Cusp forms 66 66 0
Eisenstein series 16 16 0

Trace form

\( 66 q + 30 q^{4} - 12 q^{6} - 9 q^{7} + 2 q^{9} + O(q^{10}) \) \( 66 q + 30 q^{4} - 12 q^{6} - 9 q^{7} + 2 q^{9} - 10 q^{13} - 9 q^{15} - 20 q^{16} + 2 q^{18} + 7 q^{21} + 10 q^{22} - 19 q^{25} - 48 q^{28} - 16 q^{30} - 39 q^{31} + 6 q^{36} + 11 q^{37} - 21 q^{39} + 90 q^{40} - 48 q^{42} - 12 q^{43} - 3 q^{45} + 18 q^{48} + 11 q^{49} - 10 q^{51} + 40 q^{52} - 27 q^{54} + 18 q^{55} - 26 q^{57} - 60 q^{58} + 55 q^{60} - 59 q^{63} - 68 q^{64} + 75 q^{66} - 66 q^{67} - 33 q^{69} + 20 q^{70} - 34 q^{72} + 60 q^{73} + 18 q^{75} - 12 q^{76} - 71 q^{78} + 33 q^{79} - 14 q^{81} + 12 q^{84} - 2 q^{85} + 3 q^{87} + 92 q^{88} - 75 q^{91} + 13 q^{93} + 30 q^{96} + 33 q^{97} + 22 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(273, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
273.2.bf.a 273.bf 273.af $2$ $2.180$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-5\) $\mathrm{U}(1)[D_{6}]$ \(q+(1-2\zeta_{6})q^{3}-2\zeta_{6}q^{4}+(-2-\zeta_{6})q^{7}+\cdots\)
273.2.bf.b 273.bf 273.af $64$ $2.180$ None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{6}]$