Properties

Label 546.2.by
Level $546$
Weight $2$
Character orbit 546.by
Rep. character $\chi_{546}(19,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $72$
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.by (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: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 480 72 408
Cusp forms 416 72 344
Eisenstein series 64 0 64

Trace form

\( 72q + 4q^{7} - 72q^{9} + O(q^{10}) \) \( 72q + 4q^{7} - 72q^{9} - 8q^{11} + 4q^{12} + 8q^{14} + 36q^{16} - 4q^{19} - 16q^{21} - 8q^{22} - 24q^{29} - 4q^{31} - 16q^{35} - 44q^{37} - 36q^{39} - 48q^{41} + 60q^{43} + 16q^{44} - 8q^{46} + 28q^{49} - 32q^{50} - 24q^{51} + 4q^{52} - 8q^{53} + 24q^{55} + 24q^{56} + 20q^{57} + 48q^{58} - 72q^{62} - 4q^{63} - 8q^{65} - 16q^{67} + 24q^{68} + 112q^{70} - 8q^{71} + 112q^{73} + 40q^{74} - 28q^{75} + 32q^{76} - 16q^{78} + 72q^{81} - 96q^{82} - 48q^{83} - 24q^{84} - 8q^{85} + 32q^{86} - 72q^{87} - 96q^{89} - 40q^{91} - 32q^{92} + 4q^{93} - 96q^{95} + 124q^{97} + 8q^{99} + O(q^{100}) \)

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.by.a \(32\) \(4.360\) None \(0\) \(0\) \(0\) \(8\)
546.2.by.b \(40\) \(4.360\) None \(0\) \(0\) \(0\) \(-4\)

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

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