↑

Properties

Label 273.2.t
Level $273$
Weight $2$
Character orbit 273.t
Rep. character $\chi_{273}(4,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $38$
Newform subspaces $4$
Sturm bound $74$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
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

\( 38 q + 3 q^{3} - 40 q^{4} + 4 q^{7} - 19 q^{9} + O(q^{10}) \) \( 38 q + 3 q^{3} - 40 q^{4} + 4 q^{7} - 19 q^{9} - 8 q^{10} - 12 q^{11} - 8 q^{12} - 2 q^{13} - 24 q^{14} + 28 q^{16} + 8 q^{17} + 3 q^{19} - 24 q^{20} - 7 q^{21} + 10 q^{22} - 8 q^{23} + 25 q^{25} - 26 q^{26} - 6 q^{27} + 8 q^{28} - 3 q^{31} - 2 q^{35} + 20 q^{36} + 16 q^{38} + 13 q^{39} + 14 q^{40} + 18 q^{41} + 26 q^{42} + 4 q^{43} + 12 q^{44} + 36 q^{47} + 18 q^{48} - 2 q^{49} - 102 q^{50} - 2 q^{52} - 8 q^{53} + 30 q^{55} - 6 q^{56} - 12 q^{58} + 36 q^{60} + 17 q^{61} - 40 q^{62} - 5 q^{63} - 20 q^{64} - 10 q^{65} + 16 q^{66} - 33 q^{67} + 16 q^{68} - 20 q^{69} + 36 q^{70} + 18 q^{71} - 42 q^{73} - 24 q^{74} + 26 q^{75} + 58 q^{77} - 18 q^{78} + 19 q^{79} + 48 q^{80} - 19 q^{81} + 6 q^{82} + 28 q^{84} - 48 q^{85} + 36 q^{86} - 36 q^{87} - 12 q^{88} + 16 q^{90} + 140 q^{92} + 52 q^{94} - 40 q^{95} - 30 q^{96} + 27 q^{97} + 102 q^{98} + O(q^{100}) \)

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.t.a 273.t 91.k $2$ $2.180$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-6\) \(5\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+2\zeta_{6})q^{2}+\zeta_{6}q^{3}-q^{4}+(-4+\cdots)q^{5}+\cdots\)
273.2.t.b 273.t 91.k $4$ $2.180$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(0\) \(-2\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
273.2.t.c 273.t 91.k $12$ $2.180$ 12.0.\(\cdots\).1 None \(0\) \(-6\) \(-6\) \(-3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}+\beta _{3}+\beta _{6})q^{2}+(-1-\beta _{4})q^{3}+\cdots\)
273.2.t.d 273.t 91.k $20$ $2.180$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(10\) \(6\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{2}+\beta _{3})q^{2}+\beta _{11}q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)

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

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