Properties

Label 546.2.bu
Level $546$
Weight $2$
Character orbit 546.bu
Rep. character $\chi_{546}(71,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $112$
Newform subspaces $2$
Sturm bound $224$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bu (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(224\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 480 112 368
Cusp forms 416 112 304
Eisenstein series 64 0 64

Trace form

\( 112 q + O(q^{10}) \) \( 112 q + 48 q^{10} + 48 q^{13} + 56 q^{16} - 8 q^{18} + 16 q^{19} + 8 q^{21} - 48 q^{27} - 24 q^{30} - 16 q^{31} - 24 q^{33} - 48 q^{34} - 24 q^{36} - 16 q^{37} - 80 q^{39} + 32 q^{45} - 40 q^{46} + 24 q^{54} + 16 q^{55} + 40 q^{57} + 8 q^{58} + 24 q^{60} + 16 q^{61} - 16 q^{63} + 64 q^{66} - 72 q^{69} + 16 q^{72} + 16 q^{73} + 16 q^{76} - 8 q^{78} + 32 q^{79} + 24 q^{81} - 8 q^{84} + 64 q^{85} - 16 q^{91} - 24 q^{93} - 16 q^{94} - 128 q^{97} + 16 q^{99} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
546.2.bu.a 546.bu 39.k $56$ $4.360$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
546.2.bu.b 546.bu 39.k $56$ $4.360$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

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

\( S_{2}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)