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Properties

Label 546.2.j
Level $546$
Weight $2$
Character orbit 546.j
Rep. character $\chi_{546}(289,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $36$
Newform subspaces $5$
Sturm bound $224$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 5 \)
Sturm bound: \(224\)
Trace bound: \(3\)
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 36 204
Cusp forms 208 36 172
Eisenstein series 32 0 32

Trace form

\( 36 q + 2 q^{3} + 36 q^{4} + 2 q^{7} - 18 q^{9} + O(q^{10}) \) \( 36 q + 2 q^{3} + 36 q^{4} + 2 q^{7} - 18 q^{9} + 8 q^{10} + 4 q^{11} + 2 q^{12} + 2 q^{13} + 36 q^{16} + 8 q^{17} + 6 q^{19} - 2 q^{21} - 4 q^{22} - 16 q^{23} - 6 q^{25} - 4 q^{26} - 4 q^{27} + 2 q^{28} + 4 q^{29} + 20 q^{31} - 16 q^{35} - 18 q^{36} + 68 q^{37} - 4 q^{38} - 24 q^{39} + 8 q^{40} + 4 q^{41} - 6 q^{43} + 4 q^{44} + 24 q^{46} - 24 q^{47} + 2 q^{48} + 18 q^{49} - 16 q^{50} - 12 q^{51} + 2 q^{52} - 12 q^{53} + 4 q^{55} + 20 q^{57} - 8 q^{58} - 32 q^{59} + 26 q^{61} + 20 q^{62} - 4 q^{63} + 36 q^{64} + 40 q^{65} + 16 q^{66} - 16 q^{67} + 8 q^{68} + 8 q^{69} - 64 q^{70} + 44 q^{71} - 6 q^{73} + 24 q^{74} - 44 q^{75} + 6 q^{76} - 28 q^{77} - 16 q^{78} + 24 q^{79} - 18 q^{81} + 24 q^{82} - 112 q^{83} - 2 q^{84} - 4 q^{86} - 24 q^{87} - 4 q^{88} - 16 q^{89} - 16 q^{90} + 28 q^{91} - 16 q^{92} - 56 q^{93} + 40 q^{94} - 64 q^{95} - 30 q^{97} - 24 q^{98} - 8 q^{99} + O(q^{100}) \)

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.j.a 546.j 91.h $2$ $4.360$ \(\Q(\sqrt{-3}) \) None \(2\) \(1\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+\zeta_{6}q^{3}+q^{4}+\zeta_{6}q^{6}+(2-3\zeta_{6})q^{7}+\cdots\)
546.2.j.b 546.j 91.h $8$ $4.360$ 8.0.6498455769.2 None \(-8\) \(-4\) \(-2\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}-\beta _{4}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{4}q^{6}+\cdots\)
546.2.j.c 546.j 91.h $8$ $4.360$ 8.0.447703281.1 None \(8\) \(-4\) \(2\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-1+\beta _{2})q^{3}+q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\)
546.2.j.d 546.j 91.h $8$ $4.360$ 8.0.447703281.1 None \(8\) \(4\) \(2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}-\beta _{3}q^{3}+q^{4}+(2\beta _{1}+2\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
546.2.j.e 546.j 91.h $10$ $4.360$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(5\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(1+\beta _{5})q^{3}+q^{4}-\beta _{1}q^{5}+(-1+\cdots)q^{6}+\cdots\)

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

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