Properties

Label 273.2.bt
Level $273$
Weight $2$
Character orbit 273.bt
Rep. character $\chi_{273}(136,\cdot)$
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.bt (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

\( 76q + 4q^{7} + 38q^{9} + O(q^{10}) \) \( 76q + 4q^{7} + 38q^{9} - 16q^{11} + 8q^{12} + 24q^{14} - 88q^{16} - 32q^{19} - 12q^{21} + 8q^{22} + 36q^{24} - 60q^{26} + 32q^{28} + 16q^{29} - 2q^{31} - 40q^{32} - 8q^{35} - 2q^{37} - 26q^{39} - 60q^{40} + 36q^{41} - 12q^{42} - 36q^{43} + 56q^{44} + 8q^{46} + 44q^{49} - 40q^{50} - 24q^{51} + 44q^{52} - 16q^{53} + 12q^{55} - 72q^{56} - 38q^{57} + 24q^{58} - 96q^{59} + 28q^{60} - 72q^{61} - 72q^{62} + 2q^{63} - 88q^{65} + 112q^{70} + 36q^{71} - 46q^{73} + 80q^{74} + 28q^{75} + 76q^{76} - 8q^{78} + 204q^{80} - 38q^{81} + 48q^{82} - 48q^{83} + 20q^{84} + 4q^{85} + 24q^{86} + 48q^{89} - 60q^{91} + 136q^{92} + 34q^{93} - 36q^{94} + 72q^{96} + 98q^{97} - 36q^{98} - 8q^{99} + O(q^{100}) \)

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.bt.a \(36\) \(2.180\) None \(0\) \(0\) \(0\) \(6\)
273.2.bt.b \(40\) \(2.180\) None \(0\) \(0\) \(0\) \(-2\)

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

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