Properties

Label 273.1.ch
Level $273$
Weight $1$
Character orbit 273.ch
Rep. character $\chi_{273}(80,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $4$
Newform subspaces $1$
Sturm bound $37$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 273.ch (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(37\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(273, [\chi])\).

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

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4q - 2q^{7} - 4q^{9} + O(q^{10}) \) \( 4q - 2q^{7} - 4q^{9} - 2q^{12} + 2q^{16} + 2q^{19} + 2q^{31} + 2q^{37} + 2q^{39} - 6q^{43} - 2q^{49} - 2q^{52} - 2q^{57} + 2q^{63} - 4q^{67} + 4q^{73} + 2q^{75} - 4q^{76} + 4q^{81} + 4q^{84} - 2q^{93} - 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(273, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
273.1.ch.a \(4\) \(0.136\) \(\Q(\zeta_{12})\) \(D_{12}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-\zeta_{12}^{3}q^{3}-\zeta_{12}^{5}q^{4}+\zeta_{12}^{4}q^{7}+\cdots\)