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

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

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.cg.a 273.cg 91.w $36$ $2.180$ None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{12}]$
273.2.cg.b 273.cg 91.w $40$ $2.180$ None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{12}]$

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

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