Properties

Label 273.2.bw
Level $273$
Weight $2$
Character orbit 273.bw
Rep. character $\chi_{273}(11,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $132$
Newform subspaces $2$
Sturm bound $74$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.bw (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(74\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 164 164 0
Cusp forms 132 132 0
Eisenstein series 32 32 0

Trace form

\( 132q - 4q^{3} - 12q^{4} - 4q^{6} - 16q^{7} - 4q^{9} + O(q^{10}) \) \( 132q - 4q^{3} - 12q^{4} - 4q^{6} - 16q^{7} - 4q^{9} - 36q^{12} - 16q^{13} - 6q^{15} + 40q^{16} + 22q^{18} - 14q^{19} - 24q^{21} - 8q^{22} - 4q^{24} - 40q^{27} - 72q^{28} - 12q^{31} + 50q^{33} - 48q^{34} - 60q^{36} + 8q^{37} + 16q^{39} + 44q^{40} + 44q^{42} - 108q^{43} + 58q^{45} + 48q^{46} - 64q^{48} + 2q^{49} + 36q^{51} - 20q^{52} - 22q^{54} - 16q^{55} + 10q^{57} - 28q^{58} - 4q^{60} - 40q^{61} + 20q^{63} - 34q^{66} + 74q^{67} - 54q^{69} + 64q^{70} - 98q^{72} + 62q^{73} - 42q^{75} + 116q^{76} + 82q^{78} - 24q^{79} - 12q^{81} + 4q^{84} + 56q^{85} - 2q^{87} - 22q^{91} + 16q^{93} + 32q^{94} - 54q^{96} + 62q^{97} - 10q^{99} + O(q^{100}) \)

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.bw.a \(4\) \(2.180\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+(-2\zeta_{12}+\zeta_{12}^{3})q^{3}+(-2\zeta_{12}+2\zeta_{12}^{3})q^{4}+\cdots\)
273.2.bw.b \(128\) \(2.180\) None \(0\) \(-4\) \(0\) \(-16\)