Properties

Label 546.2.bu
Level $546$
Weight $2$
Character orbit 546.bu
Rep. character $\chi_{546}(71,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $112$
Newform subspaces $2$
Sturm bound $224$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bu (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(224\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 480 112 368
Cusp forms 416 112 304
Eisenstein series 64 0 64

Trace form

\( 112q + O(q^{10}) \) \( 112q + 48q^{10} + 48q^{13} + 56q^{16} - 8q^{18} + 16q^{19} + 8q^{21} - 48q^{27} - 24q^{30} - 16q^{31} - 24q^{33} - 48q^{34} - 24q^{36} - 16q^{37} - 80q^{39} + 32q^{45} - 40q^{46} + 24q^{54} + 16q^{55} + 40q^{57} + 8q^{58} + 24q^{60} + 16q^{61} - 16q^{63} + 64q^{66} - 72q^{69} + 16q^{72} + 16q^{73} + 16q^{76} - 8q^{78} + 32q^{79} + 24q^{81} - 8q^{84} + 64q^{85} - 16q^{91} - 24q^{93} - 16q^{94} - 128q^{97} + 16q^{99} + O(q^{100}) \)

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.bu.a \(56\) \(4.360\) None \(0\) \(0\) \(0\) \(0\)
546.2.bu.b \(56\) \(4.360\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)