Properties

Label 273.2.cc
Level $273$
Weight $2$
Character orbit 273.cc
Rep. character $\chi_{273}(50,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $112$
Newform subspaces $1$
Sturm bound $74$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.cc (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(\zeta_{12})\)
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 168 112 56
Cusp forms 136 112 24
Eisenstein series 32 0 32

Trace form

\( 112q - 12q^{6} + O(q^{10}) \) \( 112q - 12q^{6} - 48q^{10} - 32q^{13} + 4q^{15} + 40q^{16} - 16q^{18} - 8q^{19} - 4q^{21} - 16q^{22} - 88q^{24} + 24q^{27} - 72q^{30} + 16q^{31} + 48q^{34} + 12q^{36} + 48q^{37} + 56q^{39} + 32q^{40} - 28q^{45} + 72q^{46} + 24q^{48} - 144q^{52} - 108q^{54} - 28q^{57} - 120q^{58} - 116q^{60} - 48q^{61} + 16q^{63} + 40q^{66} - 16q^{67} + 72q^{69} + 48q^{70} + 52q^{72} - 16q^{73} + 60q^{75} + 16q^{76} - 4q^{78} + 16q^{79} - 20q^{81} + 120q^{82} + 72q^{84} - 40q^{85} - 24q^{87} + 72q^{88} + 16q^{91} + 92q^{93} - 96q^{94} + 28q^{96} + 96q^{97} - 144q^{99} + O(q^{100}) \)

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.cc.a \(112\) \(2.180\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(273, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)