Properties

Label 273.2.cg
Level $273$
Weight $2$
Character orbit 273.cg
Rep. character $\chi_{273}(19,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $76$
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.cg (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
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 164 76 88
Cusp forms 132 76 56
Eisenstein series 32 0 32

Trace form

\( 76q - 4q^{7} - 76q^{9} + O(q^{10}) \) \( 76q - 4q^{7} - 76q^{9} + 8q^{11} - 8q^{12} + 24q^{14} + 44q^{16} - 10q^{19} + 2q^{21} + 8q^{22} - 60q^{26} + 4q^{28} + 16q^{29} + 8q^{31} + 20q^{32} + 16q^{35} + 16q^{37} + 16q^{39} - 60q^{40} - 36q^{41} + 24q^{42} - 36q^{43} - 64q^{44} - 52q^{46} - 14q^{49} - 40q^{50} + 24q^{51} + 100q^{52} - 16q^{53} - 12q^{55} + 36q^{56} - 38q^{57} - 72q^{58} - 44q^{60} + 72q^{62} + 4q^{63} + 56q^{65} + 18q^{67} - 72q^{68} - 152q^{70} + 36q^{71} - 38q^{73} - 40q^{74} + 14q^{75} - 76q^{76} - 8q^{78} + 96q^{80} + 76q^{81} + 96q^{82} + 48q^{83} + 72q^{84} + 4q^{85} - 48q^{86} + 36q^{87} + 48q^{89} + 26q^{91} + 136q^{92} - 14q^{93} + 48q^{95} + 12q^{96} - 98q^{97} - 72q^{98} - 8q^{99} + O(q^{100}) \)

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.cg.a \(36\) \(2.180\) None \(0\) \(0\) \(0\) \(4\)
273.2.cg.b \(40\) \(2.180\) None \(0\) \(0\) \(0\) \(-8\)

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

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