Properties

Label 273.2.e
Level $273$
Weight $2$
Character orbit 273.e
Rep. character $\chi_{273}(209,\cdot)$
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.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
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 32 8
Cusp forms 32 32 0
Eisenstein series 8 0 8

Trace form

\( 32q - 32q^{4} + 4q^{7} - 8q^{9} + O(q^{10}) \) \( 32q - 32q^{4} + 4q^{7} - 8q^{9} - 12q^{15} + 16q^{16} - 20q^{18} - 4q^{21} - 16q^{22} - 28q^{28} + 16q^{30} + 24q^{36} + 24q^{37} + 32q^{43} - 24q^{46} - 24q^{49} - 8q^{51} + 32q^{57} + 24q^{58} - 28q^{60} + 8q^{63} + 48q^{64} - 32q^{67} - 8q^{70} + 64q^{72} + 20q^{78} - 32q^{79} + 32q^{81} - 48q^{84} - 16q^{85} + 64q^{88} + 4q^{91} - 52q^{93} + 20q^{99} + O(q^{100}) \)

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.e.a \(32\) \(2.180\) None \(0\) \(0\) \(0\) \(4\)