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Properties

Label 273.2.j
Level $273$
Weight $2$
Character orbit 273.j
Rep. character $\chi_{273}(100,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $38$
Newform subspaces $3$
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.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 3 \)
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 82 38 44
Cusp forms 66 38 28
Eisenstein series 16 0 16

Trace form

\( 38 q + 6 q^{3} - 20 q^{4} - 3 q^{7} + 38 q^{9} + O(q^{10}) \) \( 38 q + 6 q^{3} - 20 q^{4} - 3 q^{7} + 38 q^{9} + 16 q^{10} + 8 q^{11} - 8 q^{12} + 2 q^{13} - 16 q^{14} - 30 q^{16} + 4 q^{17} + 6 q^{19} - 8 q^{20} - 5 q^{21} - 2 q^{22} - 4 q^{23} - 24 q^{24} - 25 q^{25} - 2 q^{26} + 6 q^{27} + 8 q^{28} - 11 q^{31} + 20 q^{32} - 56 q^{34} - 2 q^{35} - 20 q^{36} + 23 q^{37} + 24 q^{38} - 8 q^{39} - 34 q^{40} + 18 q^{41} - 2 q^{42} + 4 q^{43} - 20 q^{44} - 8 q^{46} + 12 q^{47} - 18 q^{48} + 3 q^{49} - 2 q^{50} + 8 q^{51} + 48 q^{52} + 24 q^{53} - 34 q^{55} + 34 q^{56} - 38 q^{57} - 40 q^{58} - 32 q^{59} + 32 q^{60} + 18 q^{61} + 16 q^{62} - 3 q^{63} + 36 q^{64} - 48 q^{65} - 16 q^{66} - 34 q^{67} + 32 q^{68} - 12 q^{69} + 76 q^{70} + 10 q^{71} + 4 q^{73} + 12 q^{74} - 29 q^{75} - 12 q^{76} - 10 q^{77} + 10 q^{78} - 19 q^{79} - 40 q^{80} + 38 q^{81} + 28 q^{82} + 64 q^{83} + 22 q^{84} - 20 q^{85} + 20 q^{86} - 30 q^{87} - 24 q^{88} + 16 q^{89} + 16 q^{90} + 13 q^{91} - 4 q^{92} - 17 q^{93} + 128 q^{94} - 36 q^{95} + 14 q^{96} + 23 q^{97} - 82 q^{98} + 8 q^{99} + O(q^{100}) \)

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.j.a 273.j 91.g $2$ $2.180$ \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{3}+(2-2\zeta_{6})q^{4}+(3-\zeta_{6})q^{7}+q^{9}+\cdots\)
273.2.j.b 273.j 91.g $16$ $2.180$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-16\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}-q^{3}+(-\beta _{3}+\beta _{5}-\beta _{9}+\beta _{14}+\cdots)q^{4}+\cdots\)
273.2.j.c 273.j 91.g $20$ $2.180$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(20\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{4})q^{2}+q^{3}+(-\beta _{2}-2\beta _{7}+\cdots)q^{4}+\cdots\)

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

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