Properties

Label 273.2.t
Level $273$
Weight $2$
Character orbit 273.t
Rep. character $\chi_{273}(4,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $38$
Newform subspaces $4$
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.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
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 38 44
Cusp forms 66 38 28
Eisenstein series 16 0 16

Trace form

\( 38q + 3q^{3} - 40q^{4} + 4q^{7} - 19q^{9} + O(q^{10}) \) \( 38q + 3q^{3} - 40q^{4} + 4q^{7} - 19q^{9} - 8q^{10} - 12q^{11} - 8q^{12} - 2q^{13} - 24q^{14} + 28q^{16} + 8q^{17} + 3q^{19} - 24q^{20} - 7q^{21} + 10q^{22} - 8q^{23} + 25q^{25} - 26q^{26} - 6q^{27} + 8q^{28} - 3q^{31} - 2q^{35} + 20q^{36} + 16q^{38} + 13q^{39} + 14q^{40} + 18q^{41} + 26q^{42} + 4q^{43} + 12q^{44} + 36q^{47} + 18q^{48} - 2q^{49} - 102q^{50} - 2q^{52} - 8q^{53} + 30q^{55} - 6q^{56} - 12q^{58} + 36q^{60} + 17q^{61} - 40q^{62} - 5q^{63} - 20q^{64} - 10q^{65} + 16q^{66} - 33q^{67} + 16q^{68} - 20q^{69} + 36q^{70} + 18q^{71} - 42q^{73} - 24q^{74} + 26q^{75} + 58q^{77} - 18q^{78} + 19q^{79} + 48q^{80} - 19q^{81} + 6q^{82} + 28q^{84} - 48q^{85} + 36q^{86} - 36q^{87} - 12q^{88} + 16q^{90} + 140q^{92} + 52q^{94} - 40q^{95} - 30q^{96} + 27q^{97} + 102q^{98} + O(q^{100}) \)

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.t.a \(2\) \(2.180\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-6\) \(5\) \(q+(-1+2\zeta_{6})q^{2}+\zeta_{6}q^{3}-q^{4}+(-4+\cdots)q^{5}+\cdots\)
273.2.t.b \(4\) \(2.180\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(0\) \(-2\) \(6\) \(0\) \(q+(\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
273.2.t.c \(12\) \(2.180\) 12.0.\(\cdots\).1 None \(0\) \(-6\) \(-6\) \(-3\) \(q+(\beta _{1}+\beta _{3}+\beta _{6})q^{2}+(-1-\beta _{4})q^{3}+\cdots\)
273.2.t.d \(20\) \(2.180\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(10\) \(6\) \(2\) \(q+(\beta _{2}+\beta _{3})q^{2}+\beta _{11}q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(273, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(273, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)