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Properties

Label 273.2.bn
Level $273$
Weight $2$
Character orbit 273.bn
Rep. character $\chi_{273}(146,\cdot)$
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.bn (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

\( 68 q + 28 q^{4} - 5 q^{7} - 4 q^{9} + O(q^{10}) \) \( 68 q + 28 q^{4} - 5 q^{7} - 4 q^{9} - 18 q^{15} - 24 q^{16} + 8 q^{18} - 26 q^{21} - 32 q^{22} + 28 q^{25} + 38 q^{28} - 40 q^{30} + 6 q^{36} - 8 q^{37} + 24 q^{39} - 12 q^{42} + 14 q^{43} - 36 q^{46} - 11 q^{49} - 28 q^{51} - 44 q^{57} - 116 q^{60} + 7 q^{63} - 16 q^{64} - 50 q^{67} - 64 q^{70} + 62 q^{72} - 2 q^{78} + 4 q^{79} - 8 q^{81} - 18 q^{84} + 28 q^{85} + 80 q^{88} - 7 q^{91} + 16 q^{93} - 32 q^{99} + O(q^{100}) \)

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