Properties

Label 273.2.bh
Level $273$
Weight $2$
Character orbit 273.bh
Rep. character $\chi_{273}(131,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $1$
Sturm bound $74$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.bh (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(74\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 84 64 20
Cusp forms 68 64 4
Eisenstein series 16 0 16

Trace form

\( 64q + 32q^{4} - 4q^{7} - 4q^{9} + O(q^{10}) \) \( 64q + 32q^{4} - 4q^{7} - 4q^{9} - 12q^{10} - 30q^{12} + 12q^{15} - 16q^{16} - 10q^{18} + 10q^{21} - 8q^{22} + 36q^{24} - 36q^{25} - 20q^{28} - 22q^{30} + 12q^{31} + 36q^{36} - 36q^{40} + 48q^{42} - 32q^{43} - 6q^{45} - 48q^{46} + 36q^{49} - 16q^{51} - 54q^{54} - 8q^{57} - 12q^{58} + 16q^{60} - 72q^{61} - 86q^{63} - 48q^{64} - 78q^{66} + 32q^{67} - 4q^{70} + 62q^{72} + 48q^{73} + 48q^{75} - 20q^{78} - 64q^{79} + 28q^{81} + 72q^{82} - 18q^{84} + 64q^{85} + 60q^{87} + 44q^{88} + 8q^{91} - 38q^{93} + 72q^{94} + 66q^{96} - 68q^{99} + O(q^{100}) \)

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.bh.a \(64\) \(2.180\) None \(0\) \(0\) \(0\) \(-4\)

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

\( S_{2}^{\mathrm{old}}(273, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)