↑

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 $2$

Related objects

Downloads

Learn more

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

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

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.i.a 273.i 7.c $2$ $2.180$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-4\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
273.2.i.b 273.i 7.c $6$ $2.180$ \(\Q(\zeta_{18})\) None \(0\) \(3\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\zeta_{18}+\zeta_{18}^{2}+\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+\cdots\)
273.2.i.c 273.i 7.c $6$ $2.180$ 6.0.64827.1 None \(2\) \(-3\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{4})q^{2}-\beta _{5}q^{3}+(2\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots\)
273.2.i.d 273.i 7.c $8$ $2.180$ 8.0.4868829729.1 None \(1\) \(-4\) \(-3\) \(9\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{3}+\beta _{6})q^{2}+\beta _{4}q^{3}+(\beta _{3}+\cdots)q^{4}+\cdots\)
273.2.i.e 273.i 7.c $10$ $2.180$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(5\) \(3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{4}-\beta _{8})q^{2}+(1-\beta _{2})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)

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

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