Properties

Label 273.2.i
Level $273$
Weight $2$
Character orbit 273.i
Rep. character $\chi_{273}(79,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $32$
Newform subspaces $5$
Sturm bound $74$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 5 \)
Sturm bound: \(74\)
Trace bound: \(2\)
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 32 52
Cusp forms 68 32 36
Eisenstein series 16 0 16

Trace form

\( 32q + 4q^{2} - 12q^{4} - 4q^{5} - 8q^{6} + 8q^{7} - 16q^{9} + O(q^{10}) \) \( 32q + 4q^{2} - 12q^{4} - 4q^{5} - 8q^{6} + 8q^{7} - 16q^{9} - 16q^{10} + 4q^{11} - 8q^{13} + 16q^{14} + 8q^{15} - 4q^{16} + 4q^{17} + 4q^{18} + 16q^{19} - 16q^{20} - 16q^{22} - 4q^{23} + 12q^{24} - 20q^{25} - 40q^{28} - 16q^{29} - 8q^{30} + 12q^{31} + 4q^{32} - 4q^{33} + 16q^{34} + 20q^{35} + 24q^{36} + 16q^{37} - 32q^{38} - 4q^{40} - 32q^{41} - 12q^{42} + 16q^{43} + 32q^{44} - 4q^{45} + 40q^{46} - 36q^{47} + 32q^{48} + 12q^{49} - 4q^{51} + 12q^{52} + 4q^{54} + 16q^{55} - 20q^{56} - 16q^{57} - 48q^{58} - 8q^{59} - 12q^{60} - 8q^{61} + 40q^{62} - 4q^{63} + 4q^{65} - 24q^{66} - 24q^{67} + 32q^{68} + 24q^{69} + 24q^{70} - 32q^{71} + 36q^{73} - 12q^{74} - 96q^{76} + 60q^{77} + 8q^{79} + 84q^{80} - 16q^{81} - 8q^{83} + 16q^{84} + 40q^{85} + 76q^{86} - 4q^{87} + 12q^{88} + 32q^{90} - 8q^{91} - 112q^{92} + 24q^{93} + 20q^{94} + 8q^{95} + 28q^{96} + 64q^{97} + 48q^{98} - 8q^{99} + O(q^{100}) \)

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.i.a \(2\) \(2.180\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-4\) \(-5\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
273.2.i.b \(6\) \(2.180\) \(\Q(\zeta_{18})\) None \(0\) \(3\) \(-3\) \(0\) \(q+(-\zeta_{18}+\zeta_{18}^{2}+\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+\cdots\)
273.2.i.c \(6\) \(2.180\) 6.0.64827.1 None \(2\) \(-3\) \(3\) \(0\) \(q+(\beta _{1}+\beta _{4})q^{2}-\beta _{5}q^{3}+(2\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots\)
273.2.i.d \(8\) \(2.180\) 8.0.4868829729.1 None \(1\) \(-4\) \(-3\) \(9\) \(q+(-\beta _{1}+\beta _{3}+\beta _{6})q^{2}+\beta _{4}q^{3}+(\beta _{3}+\cdots)q^{4}+\cdots\)
273.2.i.e \(10\) \(2.180\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(5\) \(3\) \(4\) \(q+(\beta _{4}-\beta _{8})q^{2}+(1-\beta _{2})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(273, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)