Properties

Label 546.2.bz
Level $546$
Weight $2$
Character orbit 546.bz
Rep. character $\chi_{546}(31,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $80$
Newform subspaces $2$
Sturm bound $224$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bz (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: \(7\)
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 80 400
Cusp forms 416 80 336
Eisenstein series 64 0 64

Trace form

\( 80q + 40q^{9} + O(q^{10}) \) \( 80q + 40q^{9} - 8q^{11} + 8q^{14} + 40q^{16} + 48q^{19} + 8q^{21} + 16q^{22} + 48q^{29} - 16q^{35} - 40q^{37} - 8q^{39} - 8q^{44} + 16q^{46} + 64q^{50} - 8q^{53} - 32q^{57} + 24q^{58} - 24q^{61} + 16q^{65} - 24q^{67} - 24q^{68} + 16q^{70} + 16q^{71} - 24q^{73} - 80q^{74} - 16q^{78} - 40q^{81} - 16q^{84} - 80q^{85} - 40q^{86} - 144q^{87} - 96q^{89} - 16q^{91} - 32q^{92} - 72q^{94} - 16q^{99} + O(q^{100}) \)

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.bz.a \(40\) \(4.360\) None \(0\) \(0\) \(0\) \(-4\)
546.2.bz.b \(40\) \(4.360\) None \(0\) \(0\) \(0\) \(4\)

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

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