Properties

Label 273.2.r
Level $273$
Weight $2$
Character orbit 273.r
Rep. character $\chi_{273}(68,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $66$
Newform subspaces $2$
Sturm bound $74$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.r (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

\( 66 q - 3 q^{3} - 60 q^{4} + 12 q^{6} - 6 q^{7} - q^{9} + O(q^{10}) \) \( 66 q - 3 q^{3} - 60 q^{4} + 12 q^{6} - 6 q^{7} - q^{9} - 6 q^{10} + 10 q^{13} - 9 q^{15} + 40 q^{16} + 2 q^{18} - 21 q^{19} + 7 q^{21} + 10 q^{22} - 18 q^{24} - 19 q^{25} - 6 q^{28} + 8 q^{30} - 39 q^{31} - 45 q^{33} + 6 q^{36} - 22 q^{37} + 30 q^{39} + 90 q^{40} + 3 q^{42} - 12 q^{43} - 18 q^{48} - 4 q^{49} - 10 q^{51} - 52 q^{52} - 18 q^{55} - 26 q^{57} + 30 q^{58} + 55 q^{60} - 45 q^{61} + 28 q^{63} - 68 q^{64} + 75 q^{66} + 33 q^{67} + 33 q^{69} + 20 q^{70} + 17 q^{72} + 60 q^{73} + 12 q^{76} - 71 q^{78} + 33 q^{79} + 7 q^{81} - 18 q^{82} - 141 q^{84} - 2 q^{85} - 46 q^{88} - 2 q^{91} - 26 q^{93} + 36 q^{94} + 30 q^{96} - 33 q^{97} + 22 q^{99} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
273.2.r.a 273.r 273.r $2$ $2.180$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) 273.2.r.a \(0\) \(-3\) \(0\) \(4\) $\mathrm{U}(1)[D_{6}]$ \(q+(-1-\zeta_{6})q^{3}+2q^{4}+(1+2\zeta_{6})q^{7}+\cdots\)
273.2.r.b 273.r 273.r $64$ $2.180$ None 273.2.r.b \(0\) \(0\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{6}]$