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

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

Decomposition of \(S_{2}^{\mathrm{new}}(273, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
273.2.bn.a \(2\) \(2.180\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-3\) \(0\) \(-5\) \(q+(-2+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(-2+\cdots)q^{7}+\cdots\)
273.2.bn.b \(2\) \(2.180\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(4\) \(q+(2-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(1+2\zeta_{6})q^{7}+\cdots\)
273.2.bn.c \(64\) \(2.180\) None \(0\) \(0\) \(0\) \(-4\)