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

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

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.br.a \(2\) \(2.180\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(4\) \(q+(2-\zeta_{6})q^{3}-2q^{4}+(3-2\zeta_{6})q^{7}+\cdots\)
273.2.br.b \(64\) \(2.180\) None \(0\) \(-6\) \(0\) \(-6\)