Properties

Label 273.2.bz
Level $273$
Weight $2$
Character orbit 273.bz
Rep. character $\chi_{273}(31,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $72$
Newform subspaces $2$
Sturm bound $74$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.bz (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(74\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 168 72 96
Cusp forms 136 72 64
Eisenstein series 32 0 32

Trace form

\( 72q - 2q^{7} + 36q^{9} + O(q^{10}) \) \( 72q - 2q^{7} + 36q^{9} + 8q^{11} - 72q^{14} + 24q^{16} - 30q^{19} + 8q^{21} - 16q^{22} - 36q^{24} - 60q^{26} + 16q^{28} - 32q^{29} - 6q^{31} + 20q^{32} + 16q^{35} + 14q^{37} + 2q^{39} + 120q^{40} + 24q^{42} + 8q^{44} - 16q^{46} - 136q^{50} - 144q^{52} - 16q^{53} - 12q^{57} - 48q^{58} + 96q^{59} - 44q^{60} + 72q^{61} + 2q^{63} - 16q^{65} - 2q^{67} + 72q^{68} - 104q^{70} - 72q^{71} - 54q^{73} + 80q^{74} + 64q^{78} - 12q^{80} - 36q^{81} + 20q^{84} + 88q^{85} + 24q^{86} + 72q^{87} + 48q^{89} - 10q^{91} - 80q^{92} + 6q^{93} + 132q^{96} + 96q^{98} + 16q^{99} + O(q^{100}) \)

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.bz.a \(36\) \(2.180\) None \(0\) \(0\) \(0\) \(-6\)
273.2.bz.b \(36\) \(2.180\) None \(0\) \(0\) \(0\) \(4\)

Decomposition of \(S_{2}^{\mathrm{old}}(273, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(273, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)