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

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

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.y.a \(2\) \(2.180\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(5\) \(q+(1-2\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+(3-\zeta_{6})q^{7}+\cdots\)
273.2.y.b \(64\) \(2.180\) None \(0\) \(0\) \(0\) \(-12\)