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Properties

Label 273.2.ba
Level $273$
Weight $2$
Character orbit 273.ba
Rep. character $\chi_{273}(38,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $68$
Newform subspaces $3$
Sturm bound $74$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.ba (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: \(7\)
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

\( 68 q - 6 q^{3} - 36 q^{4} - 6 q^{9} + O(q^{10}) \) \( 68 q - 6 q^{3} - 36 q^{4} - 6 q^{9} - 12 q^{10} + 6 q^{12} - 40 q^{16} - 24 q^{22} + 18 q^{25} - 22 q^{30} + 68 q^{36} + 9 q^{39} - 108 q^{40} + 24 q^{42} - 20 q^{43} - 6 q^{49} + 28 q^{51} + 30 q^{52} + 24 q^{61} + 90 q^{66} - 90 q^{75} - 68 q^{78} - 10 q^{79} + 42 q^{81} + 120 q^{82} + 60 q^{87} + 12 q^{88} - 39 q^{91} + 168 q^{94} + O(q^{100}) \)

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.ba.a 273.ba 273.aa $2$ $2.180$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(-1\) $\mathrm{U}(1)[D_{6}]$ \(q+(1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+(-2+3\zeta_{6})q^{7}+\cdots\)
273.2.ba.b 273.ba 273.aa $2$ $2.180$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(1\) $\mathrm{U}(1)[D_{6}]$ \(q+(1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+(2-3\zeta_{6})q^{7}+\cdots\)
273.2.ba.c 273.ba 273.aa $64$ $2.180$ None \(0\) \(-12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$