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Properties

Label 273.2.k
Level $273$
Weight $2$
Character orbit 273.k
Rep. character $\chi_{273}(22,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $24$
Newform subspaces $4$
Sturm bound $74$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.k (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(74\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(273, [\chi])\).

Total New Old
Modular forms 84 24 60
Cusp forms 68 24 44
Eisenstein series 16 0 16

Trace form

\( 24 q + 4 q^{2} - 8 q^{4} + 16 q^{5} - 24 q^{8} - 12 q^{9} + O(q^{10}) \) \( 24 q + 4 q^{2} - 8 q^{4} + 16 q^{5} - 24 q^{8} - 12 q^{9} + 4 q^{10} - 4 q^{11} - 16 q^{12} + 4 q^{13} - 4 q^{15} + 8 q^{16} - 20 q^{17} - 8 q^{18} + 8 q^{19} + 20 q^{20} - 4 q^{22} - 8 q^{23} + 40 q^{25} - 20 q^{26} - 12 q^{29} + 16 q^{30} - 8 q^{31} - 12 q^{32} - 4 q^{33} + 32 q^{34} + 4 q^{35} - 8 q^{36} - 8 q^{37} + 56 q^{38} + 8 q^{39} + 16 q^{40} - 16 q^{41} + 4 q^{42} + 28 q^{43} - 48 q^{44} - 8 q^{45} + 20 q^{46} - 48 q^{47} - 12 q^{49} - 4 q^{50} - 24 q^{51} - 20 q^{52} + 16 q^{53} - 12 q^{55} - 32 q^{58} - 12 q^{59} + 56 q^{60} - 24 q^{61} + 44 q^{62} - 88 q^{64} - 20 q^{65} + 32 q^{66} - 20 q^{67} - 28 q^{68} - 4 q^{69} - 48 q^{70} + 12 q^{72} + 16 q^{73} + 20 q^{74} + 16 q^{75} + 40 q^{76} + 16 q^{77} + 24 q^{78} - 40 q^{79} + 4 q^{80} - 12 q^{81} + 16 q^{82} + 112 q^{83} - 4 q^{85} + 80 q^{86} - 8 q^{87} - 12 q^{88} + 48 q^{89} - 8 q^{90} - 8 q^{91} + 40 q^{92} - 24 q^{94} - 4 q^{95} + 40 q^{96} + 4 q^{97} + 4 q^{98} + 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.k.a 273.k 13.c $6$ $2.180$ \(\Q(\zeta_{18})\) None \(0\) \(-3\) \(12\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\zeta_{18}-\zeta_{18}^{2}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots\)
273.2.k.b 273.k 13.c $6$ $2.180$ 6.0.6040683.1 None \(0\) \(3\) \(4\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{2})q^{2}+(1-\beta _{4})q^{3}+(\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
273.2.k.c 273.k 13.c $6$ $2.180$ 6.0.64827.1 None \(2\) \(-3\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{4})q^{2}+(-1+\beta _{5})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots\)
273.2.k.d 273.k 13.c $6$ $2.180$ 6.0.771147.1 None \(2\) \(3\) \(0\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}-\beta _{4}q^{3}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(273, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)