↑

Properties

Label 546.2.bx
Level $546$
Weight $2$
Character orbit 546.bx
Rep. character $\chi_{546}(97,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $80$
Newform subspaces $2$
Sturm bound $224$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bx (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(224\)
Trace bound: \(7\)
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 80 400
Cusp forms 416 80 336
Eisenstein series 64 0 64

Trace form

\( 80 q + 40 q^{9} + O(q^{10}) \) \( 80 q + 40 q^{9} + 16 q^{11} - 16 q^{14} + 40 q^{16} + 8 q^{21} + 16 q^{22} + 8 q^{35} + 80 q^{37} - 32 q^{39} + 48 q^{43} + 16 q^{44} - 8 q^{46} - 24 q^{49} - 32 q^{50} + 64 q^{53} + 24 q^{56} + 16 q^{57} - 72 q^{58} - 32 q^{65} + 16 q^{70} - 80 q^{71} + 16 q^{74} - 16 q^{78} - 96 q^{79} - 40 q^{81} - 16 q^{84} + 16 q^{85} - 16 q^{86} - 16 q^{91} - 32 q^{92} - 48 q^{93} - 192 q^{95} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.bx.a 546.bx 91.ac $40$ $4.360$ None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{12}]$
546.2.bx.b 546.bx 91.ac $40$ $4.360$ None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{12}]$

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

\( S_{2}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)