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

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

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
546.2.bg.a 546.bg 273.aa $36$ $4.360$ None 546.2.bg.a \(-18\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
546.2.bg.b 546.bg 273.aa $36$ $4.360$ None 546.2.bg.a \(18\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

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