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

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

Decomposition of \(S_{2}^{\mathrm{new}}(273, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
273.2.bt.a 273.bt 91.aa $36$ $2.180$ None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{12}]$
273.2.bt.b 273.bt 91.aa $40$ $2.180$ None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{12}]$

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

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