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 $1$

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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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
273.2.r.a \(2\) \(2.180\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-3\) \(0\) \(4\) \(q+(-1-\zeta_{6})q^{3}+2q^{4}+(1+2\zeta_{6})q^{7}+\cdots\)
273.2.r.b \(64\) \(2.180\) None \(0\) \(0\) \(0\) \(-10\)