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Properties

Label 546.2.s
Level $546$
Weight $2$
Character orbit 546.s
Rep. character $\chi_{546}(43,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $24$
Newform subspaces $5$
Sturm bound $224$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(224\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

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

Total New Old
Modular forms 240 24 216
Cusp forms 208 24 184
Eisenstein series 32 0 32

Trace form

\( 24 q + 12 q^{4} - 12 q^{9} + O(q^{10}) \) \( 24 q + 12 q^{4} - 12 q^{9} + 24 q^{11} + 8 q^{13} + 24 q^{15} - 12 q^{16} + 8 q^{17} + 8 q^{22} + 8 q^{23} - 40 q^{25} - 8 q^{30} - 24 q^{33} - 8 q^{35} + 12 q^{36} + 16 q^{38} + 8 q^{39} - 24 q^{41} + 4 q^{42} - 12 q^{43} + 12 q^{46} + 12 q^{49} + 8 q^{51} + 16 q^{52} - 64 q^{53} - 8 q^{55} - 24 q^{58} + 96 q^{59} + 8 q^{61} - 24 q^{64} + 24 q^{65} - 16 q^{66} + 36 q^{67} - 8 q^{68} - 8 q^{69} + 24 q^{71} - 8 q^{74} - 32 q^{77} + 8 q^{78} + 32 q^{79} - 12 q^{81} + 8 q^{82} - 72 q^{85} - 16 q^{87} - 8 q^{88} - 72 q^{89} + 8 q^{91} + 16 q^{92} - 16 q^{94} - 48 q^{95} + O(q^{100}) \)

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.s.a 546.s 13.e $4$ $4.360$ \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(-1+\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
546.2.s.b 546.s 13.e $4$ $4.360$ \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(-1+\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
546.2.s.c 546.s 13.e $4$ $4.360$ \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(-1+\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
546.2.s.d 546.s 13.e $4$ $4.360$ \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(1-\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
546.2.s.e 546.s 13.e $8$ $4.360$ 8.0.195105024.2 None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{2}q^{2}+(1+\beta _{4})q^{3}-\beta _{4}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)