Properties

Label 546.2.bm
Level $546$
Weight $2$
Character orbit 546.bm
Rep. character $\chi_{546}(205,\cdot)$
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.bm (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

\( 36q - 2q^{3} - 36q^{4} - 2q^{7} - 18q^{9} + O(q^{10}) \) \( 36q - 2q^{3} - 36q^{4} - 2q^{7} - 18q^{9} + 8q^{10} + 12q^{11} + 2q^{12} - 2q^{13} + 8q^{14} + 36q^{16} - 8q^{17} + 6q^{19} + 14q^{21} - 4q^{22} + 16q^{23} + 6q^{25} + 4q^{26} + 4q^{27} + 2q^{28} + 4q^{29} + 8q^{35} + 18q^{36} + 4q^{38} - 24q^{39} - 8q^{40} - 36q^{41} - 14q^{43} - 12q^{44} - 72q^{47} - 2q^{48} + 2q^{49} + 48q^{50} + 4q^{51} + 2q^{52} + 20q^{53} + 4q^{55} - 8q^{56} + 48q^{58} - 2q^{61} + 4q^{62} + 4q^{63} - 36q^{64} + 32q^{65} - 16q^{66} + 60q^{67} + 8q^{68} + 24q^{69} + 48q^{70} - 36q^{71} + 42q^{73} + 24q^{74} - 12q^{75} - 6q^{76} - 68q^{77} - 24q^{79} - 18q^{81} + 24q^{82} - 14q^{84} + 72q^{85} - 36q^{86} - 24q^{87} + 4q^{88} - 16q^{90} - 12q^{91} - 16q^{92} - 40q^{94} - 102q^{97} - 72q^{98} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
546.2.bm.a \(16\) \(4.360\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(8\) \(0\) \(-2\) \(q+(\beta _{12}+\beta _{13})q^{2}+\beta _{3}q^{3}-q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
546.2.bm.b \(20\) \(4.360\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(-10\) \(0\) \(0\) \(q+(-\beta _{10}+\beta _{11})q^{2}+\beta _{12}q^{3}-q^{4}+\cdots\)

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

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