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Properties

Label 273.2.u
Level $273$
Weight $2$
Character orbit 273.u
Rep. character $\chi_{273}(62,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $68$
Newform subspaces $3$
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.u (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(74\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(19\)

Dimensions

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

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

Trace form

\( 68 q - 36 q^{4} - 9 q^{7} + O(q^{10}) \) \( 68 q - 36 q^{4} - 9 q^{7} + 18 q^{15} - 40 q^{16} + 24 q^{22} - 60 q^{25} - 6 q^{28} + 20 q^{30} + 38 q^{36} - 12 q^{37} - 36 q^{39} + 22 q^{43} - 84 q^{46} - 3 q^{49} + 52 q^{51} - 48 q^{58} - 63 q^{63} + 144 q^{64} + 18 q^{67} - 66 q^{72} + 166 q^{78} - 52 q^{79} - 48 q^{81} + 66 q^{84} + 132 q^{85} - 15 q^{91} - 120 q^{93} + O(q^{100}) \)

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.u.a 273.u 273.u $2$ $2.180$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-3\) \(0\) \(-4\) $\mathrm{U}(1)[D_{6}]$ \(q+(-1-\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(-3+2\zeta_{6})q^{7}+\cdots\)
273.2.u.b 273.u 273.u $2$ $2.180$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(-5\) $\mathrm{U}(1)[D_{6}]$ \(q+(1+\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(-3+\zeta_{6})q^{7}+\cdots\)
273.2.u.c 273.u 273.u $64$ $2.180$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$