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Properties

Label 546.2.bd
Level $546$
Weight $2$
Character orbit 546.bd
Rep. character $\chi_{546}(121,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $36$
Newform subspaces $2$
Sturm bound $224$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bd (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(224\)
Trace bound: \(1\)
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

\( 36 q + 4 q^{3} + 18 q^{4} + 2 q^{7} + 36 q^{9} + O(q^{10}) \) \( 36 q + 4 q^{3} + 18 q^{4} + 2 q^{7} + 36 q^{9} - 16 q^{10} + 2 q^{12} - 2 q^{13} + 8 q^{14} - 18 q^{16} + 4 q^{17} - 14 q^{21} - 4 q^{22} - 8 q^{23} + 6 q^{25} + 4 q^{26} + 4 q^{27} + 4 q^{28} + 4 q^{29} + 20 q^{35} + 18 q^{36} + 30 q^{37} + 4 q^{38} + 18 q^{39} - 8 q^{40} - 36 q^{41} - 14 q^{43} + 12 q^{44} - 12 q^{46} + 72 q^{47} - 2 q^{48} + 2 q^{49} + 48 q^{50} + 4 q^{51} + 2 q^{52} + 20 q^{53} + 4 q^{55} + 4 q^{56} + 4 q^{61} + 4 q^{62} + 2 q^{63} - 36 q^{64} - 28 q^{65} - 16 q^{66} - 4 q^{68} + 24 q^{69} - 48 q^{70} - 36 q^{71} - 42 q^{73} - 12 q^{74} + 6 q^{75} - 6 q^{76} - 68 q^{77} - 24 q^{79} + 36 q^{81} - 48 q^{82} - 16 q^{84} + 72 q^{85} + 36 q^{86} + 12 q^{87} - 8 q^{88} - 24 q^{89} - 16 q^{90} - 112 q^{91} - 16 q^{92} - 24 q^{93} + 80 q^{94} - 102 q^{97} - 24 q^{98} + O(q^{100}) \)

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.bd.a 546.bd 91.u $16$ $4.360$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-16\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{13}q^{2}-q^{3}+\beta _{3}q^{4}+(-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots\)
546.2.bd.b 546.bd 91.u $20$ $4.360$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(20\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{10}q^{2}+q^{3}-\beta _{12}q^{4}+\beta _{4}q^{5}+\cdots\)

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

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