Properties

Label 273.1.s
Level $273$
Weight $1$
Character orbit 273.s
Rep. character $\chi_{273}(74,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $6$
Newform subspaces $2$
Sturm bound $37$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 273.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(37\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 14 14 0
Cusp forms 6 6 0
Eisenstein series 8 8 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 4 0 0

Trace form

\( 6q - q^{3} + 2q^{4} - 2q^{6} - 3q^{7} + q^{9} + O(q^{10}) \) \( 6q - q^{3} + 2q^{4} - 2q^{6} - 3q^{7} + q^{9} + 2q^{10} - q^{12} - 5q^{13} - 2q^{15} - 2q^{16} + q^{19} - q^{21} - 2q^{24} - q^{25} + 2q^{27} - q^{28} + 4q^{34} - q^{36} + 2q^{37} + 2q^{39} + 2q^{40} + 4q^{42} - q^{43} + 4q^{46} - q^{48} - 3q^{49} + 2q^{51} - q^{52} - 4q^{54} - 2q^{57} - 2q^{58} + q^{61} + 4q^{63} - 2q^{64} - 2q^{67} + 2q^{69} - 4q^{70} - q^{73} + 2q^{75} + q^{76} + 2q^{78} - 4q^{79} - 3q^{81} + 2q^{82} - q^{84} - 2q^{85} - 4q^{87} + 4q^{90} + 4q^{91} + 4q^{93} + 2q^{94} + 3q^{97} + O(q^{100}) \)

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.s.a \(2\) \(0.136\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q+\zeta_{6}^{2}q^{3}+q^{4}+\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots\)
273.1.s.b \(4\) \(0.136\) \(\Q(\zeta_{12})\) \(A_{4}\) None None \(0\) \(0\) \(0\) \(-2\) \(q-\zeta_{12}^{3}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{5}q^{5}+\cdots\)