Properties

Label 546.2.bb
Level $546$
Weight $2$
Character orbit 546.bb
Rep. character $\chi_{546}(269,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $76$
Newform subspaces $1$
Sturm bound $224$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(224\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(546, [\chi])\).

Total New Old
Modular forms 240 76 164
Cusp forms 208 76 132
Eisenstein series 32 0 32

Trace form

\( 76q - 76q^{4} + 10q^{7} + 4q^{9} + O(q^{10}) \) \( 76q - 76q^{4} + 10q^{7} + 4q^{9} - 2q^{13} + 12q^{15} + 76q^{16} + 18q^{19} - 8q^{21} - 42q^{25} - 10q^{28} - 10q^{30} + 12q^{31} + 72q^{33} - 4q^{36} + 12q^{37} - 42q^{39} + 2q^{42} - 2q^{43} + 8q^{46} - 10q^{49} + 10q^{51} + 2q^{52} - 24q^{55} + 8q^{57} - 8q^{58} - 12q^{60} + 78q^{61} + 2q^{63} - 76q^{64} - 24q^{66} - 48q^{67} + 30q^{69} - 54q^{73} - 18q^{76} - 12q^{78} - 60q^{79} - 4q^{81} - 24q^{82} + 8q^{84} + 8q^{85} - 8q^{91} - 32q^{93} - 24q^{94} + 66q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(546, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
546.2.bb.a \(76\) \(4.360\) None \(0\) \(0\) \(0\) \(10\)

Decomposition of \(S_{2}^{\mathrm{old}}(546, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)