Properties

Label 273.2.l
Level $273$
Weight $2$
Character orbit 273.l
Rep. character $\chi_{273}(16,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $38$
Newform subspaces $3$
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.l (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 3 \)
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

\( 38q - 3q^{3} + 40q^{4} - 19q^{9} + O(q^{10}) \) \( 38q - 3q^{3} + 40q^{4} - 19q^{9} - 8q^{10} - 4q^{11} - 8q^{12} + 2q^{13} - 16q^{14} + 60q^{16} - 8q^{17} - 3q^{19} - 8q^{20} - 5q^{21} - 2q^{22} + 8q^{23} + 12q^{24} - 25q^{25} + 46q^{26} + 6q^{27} - 16q^{28} - 11q^{31} - 40q^{32} - 56q^{34} + 10q^{35} - 20q^{36} - 46q^{37} + 24q^{38} + 13q^{39} - 34q^{40} + 18q^{41} - 14q^{42} + 4q^{43} - 20q^{44} + 16q^{46} + 12q^{47} - 18q^{48} + 6q^{49} - 2q^{50} + 8q^{51} - 66q^{52} + 24q^{53} - 34q^{55} - 74q^{56} - 38q^{57} + 20q^{58} + 64q^{59} + 32q^{60} - 9q^{61} + 16q^{62} + 3q^{63} + 36q^{64} - 30q^{65} - 16q^{66} + 17q^{67} - 64q^{68} - 12q^{69} + 76q^{70} + 10q^{71} + 4q^{73} - 24q^{74} + 58q^{75} - 12q^{76} - 10q^{77} + 10q^{78} - 19q^{79} + 20q^{80} - 19q^{81} - 14q^{82} + 64q^{83} - 8q^{84} - 20q^{85} + 20q^{86} + 60q^{87} + 12q^{88} - 32q^{89} + 16q^{90} + 4q^{91} - 4q^{92} + 34q^{93} - 64q^{94} + 72q^{95} + 14q^{96} + 23q^{97} - 58q^{98} + 8q^{99} + O(q^{100}) \)

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.l.a \(2\) \(2.180\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-4\) \(q-\zeta_{6}q^{3}-2q^{4}+(-3+2\zeta_{6})q^{7}+(-1+\cdots)q^{9}+\cdots\)
273.2.l.b \(16\) \(2.180\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(8\) \(0\) \(1\) \(q+(-\beta _{1}-\beta _{2})q^{2}+\beta _{9}q^{3}+(1+\beta _{3}+\cdots)q^{4}+\cdots\)
273.2.l.c \(20\) \(2.180\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(-10\) \(0\) \(3\) \(q-\beta _{4}q^{2}+(-1+\beta _{7})q^{3}+(2+\beta _{2})q^{4}+\cdots\)

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

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