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Properties

Label 273.2.br
Level $273$
Weight $2$
Character orbit 273.br
Rep. character $\chi_{273}(17,\cdot)$
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.br (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

\( 66 q - 3 q^{3} + 52 q^{4} - 2 q^{7} + 3 q^{9} + O(q^{10}) \) \( 66 q - 3 q^{3} + 52 q^{4} - 2 q^{7} + 3 q^{9} - 6 q^{10} - 12 q^{12} - 10 q^{13} - 9 q^{15} + 24 q^{16} - 36 q^{18} + q^{19} - 9 q^{21} - 18 q^{22} - 12 q^{24} + 11 q^{25} + 10 q^{28} - 22 q^{30} + 29 q^{31} - 15 q^{33} - 24 q^{34} - 10 q^{36} - 12 q^{39} - 54 q^{40} + 39 q^{42} - 4 q^{43} - 6 q^{45} - 42 q^{48} + 4 q^{49} - 14 q^{51} - 52 q^{52} + 18 q^{54} + 42 q^{55} + 30 q^{58} - 9 q^{60} + 33 q^{61} - 44 q^{64} - 9 q^{66} + 27 q^{67} - 39 q^{69} - 84 q^{70} - 123 q^{72} - 22 q^{73} + 16 q^{76} - 11 q^{78} - 9 q^{79} - 9 q^{81} - 66 q^{82} + 21 q^{84} - 30 q^{85} - 30 q^{88} + 122 q^{91} + 84 q^{94} - 24 q^{96} + 7 q^{97} + O(q^{100}) \)

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.br.a 273.br 273.ar $2$ $2.180$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(4\) $\mathrm{U}(1)[D_{6}]$ \(q+(2-\zeta_{6})q^{3}-2q^{4}+(3-2\zeta_{6})q^{7}+\cdots\)
273.2.br.b 273.br 273.ar $64$ $2.180$ None \(0\) \(-6\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$