Properties

Label 273.2.y
Level $273$
Weight $2$
Character orbit 273.y
Rep. character $\chi_{273}(101,\cdot)$
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.y (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

\( 66 q - 26 q^{4} - 7 q^{7} - 6 q^{9} + O(q^{10}) \) \( 66 q - 26 q^{4} - 7 q^{7} - 6 q^{9} - 12 q^{12} + 10 q^{13} - 9 q^{15} - 12 q^{16} + 36 q^{18} + 2 q^{19} + 9 q^{21} - 18 q^{22} - 24 q^{24} + 11 q^{25} + 8 q^{28} + 44 q^{30} - 29 q^{31} - 30 q^{33} + 24 q^{34} - 10 q^{36} - 27 q^{37} - 15 q^{39} - 54 q^{40} - 24 q^{42} - 4 q^{43} - 3 q^{45} - 24 q^{46} + 42 q^{48} + 19 q^{49} - 14 q^{51} + 4 q^{52} + 9 q^{54} - 42 q^{55} + 9 q^{60} - 9 q^{63} - 44 q^{64} - 9 q^{66} + 39 q^{69} + 84 q^{70} + 22 q^{73} + 36 q^{75} - 16 q^{76} - 11 q^{78} - 9 q^{79} + 18 q^{81} + 12 q^{84} - 30 q^{85} + 3 q^{87} + 60 q^{88} + 5 q^{91} + 3 q^{93} + 24 q^{96} - 7 q^{97} + O(q^{100}) \)

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.y.a 273.y 273.y $2$ $2.180$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(5\) $\mathrm{U}(1)[D_{6}]$ \(q+(1-2\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+(3-\zeta_{6})q^{7}+\cdots\)
273.2.y.b 273.y 273.y $64$ $2.180$ None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{6}]$