Properties

Label 546.2.bg
Level $546$
Weight $2$
Character orbit 546.bg
Rep. character $\chi_{546}(311,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $72$
Newform subspaces $2$
Sturm bound $224$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bg (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(224\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 240 72 168
Cusp forms 208 72 136
Eisenstein series 32 0 32

Trace form

\( 72q - 36q^{4} + 8q^{9} + O(q^{10}) \) \( 72q - 36q^{4} + 8q^{9} - 36q^{16} + 28q^{25} + 14q^{30} - 16q^{36} - 32q^{42} - 32q^{43} + 24q^{49} - 6q^{51} + 12q^{52} - 72q^{61} + 72q^{64} - 48q^{66} + 108q^{75} + 40q^{78} + 40q^{79} - 40q^{81} - 48q^{82} - 48q^{87} - 4q^{91} - 144q^{94} + O(q^{100}) \)

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.bg.a \(36\) \(4.360\) None \(-18\) \(0\) \(0\) \(0\)
546.2.bg.b \(36\) \(4.360\) None \(18\) \(0\) \(0\) \(0\)

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

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