Properties

Label 273.2.g
Level $273$
Weight $2$
Character orbit 273.g
Rep. character $\chi_{273}(272,\cdot)$
Character field $\Q$
Dimension $32$
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.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q\)
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 40 40 0
Cusp forms 32 32 0
Eisenstein series 8 8 0

Trace form

\( 32q + 16q^{4} + O(q^{10}) \) \( 32q + 16q^{4} - 16q^{16} - 16q^{25} + 16q^{30} - 32q^{36} - 48q^{42} + 48q^{43} - 32q^{49} - 16q^{51} - 80q^{64} + 32q^{78} + 80q^{79} - 48q^{81} - 96q^{88} + 32q^{91} + O(q^{100}) \)

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.g.a \(32\) \(2.180\) None \(0\) \(0\) \(0\) \(0\)