Properties

Label 273.2.j
Level $273$
Weight $2$
Character orbit 273.j
Rep. character $\chi_{273}(100,\cdot)$
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.j (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

\( 38q + 6q^{3} - 20q^{4} - 3q^{7} + 38q^{9} + O(q^{10}) \) \( 38q + 6q^{3} - 20q^{4} - 3q^{7} + 38q^{9} + 16q^{10} + 8q^{11} - 8q^{12} + 2q^{13} - 16q^{14} - 30q^{16} + 4q^{17} + 6q^{19} - 8q^{20} - 5q^{21} - 2q^{22} - 4q^{23} - 24q^{24} - 25q^{25} - 2q^{26} + 6q^{27} + 8q^{28} - 11q^{31} + 20q^{32} - 56q^{34} - 2q^{35} - 20q^{36} + 23q^{37} + 24q^{38} - 8q^{39} - 34q^{40} + 18q^{41} - 2q^{42} + 4q^{43} - 20q^{44} - 8q^{46} + 12q^{47} - 18q^{48} + 3q^{49} - 2q^{50} + 8q^{51} + 48q^{52} + 24q^{53} - 34q^{55} + 34q^{56} - 38q^{57} - 40q^{58} - 32q^{59} + 32q^{60} + 18q^{61} + 16q^{62} - 3q^{63} + 36q^{64} - 48q^{65} - 16q^{66} - 34q^{67} + 32q^{68} - 12q^{69} + 76q^{70} + 10q^{71} + 4q^{73} + 12q^{74} - 29q^{75} - 12q^{76} - 10q^{77} + 10q^{78} - 19q^{79} - 40q^{80} + 38q^{81} + 28q^{82} + 64q^{83} + 22q^{84} - 20q^{85} + 20q^{86} - 30q^{87} - 24q^{88} + 16q^{89} + 16q^{90} + 13q^{91} - 4q^{92} - 17q^{93} + 128q^{94} - 36q^{95} + 14q^{96} + 23q^{97} - 82q^{98} + 8q^{99} + O(q^{100}) \)

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.j.a \(2\) \(2.180\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(5\) \(q+q^{3}+(2-2\zeta_{6})q^{4}+(3-\zeta_{6})q^{7}+q^{9}+\cdots\)
273.2.j.b \(16\) \(2.180\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-16\) \(0\) \(1\) \(q+\beta _{1}q^{2}-q^{3}+(-\beta _{3}+\beta _{5}-\beta _{9}+\beta _{14}+\cdots)q^{4}+\cdots\)
273.2.j.c \(20\) \(2.180\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(20\) \(0\) \(-9\) \(q+(\beta _{1}+\beta _{4})q^{2}+q^{3}+(-\beta _{2}-2\beta _{7}+\cdots)q^{4}+\cdots\)

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

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