Properties

Label 546.2.bq
Level $546$
Weight $2$
Character orbit 546.bq
Rep. character $\chi_{546}(419,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $72$
Newform subspaces $3$
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.bq (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(224\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(5\), \(61\)

Dimensions

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

Total New Old
Modular forms 240 72 168
Cusp forms 208 72 136
Eisenstein series 32 0 32

Trace form

\( 72q + 36q^{4} + 8q^{7} + 4q^{9} + O(q^{10}) \) \( 72q + 36q^{4} + 8q^{7} + 4q^{9} + 12q^{15} - 36q^{16} - 24q^{18} + 16q^{21} + 56q^{25} - 8q^{28} + 8q^{30} - 4q^{36} - 16q^{37} - 48q^{39} + 8q^{42} - 12q^{43} - 4q^{46} + 4q^{49} + 16q^{51} + 8q^{57} - 8q^{58} + 24q^{60} + 8q^{63} - 72q^{64} + 52q^{67} - 12q^{72} + 36q^{78} + 16q^{79} + 32q^{81} + 8q^{84} - 88q^{85} - 64q^{91} - 56q^{93} + O(q^{100}) \)

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.bq.a \(4\) \(4.360\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(2\) \(q+\zeta_{12}q^{2}+(-\zeta_{12}+2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
546.2.bq.b \(4\) \(4.360\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-10\) \(q+\zeta_{12}q^{2}+(\zeta_{12}-2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
546.2.bq.c \(64\) \(4.360\) None \(0\) \(0\) \(0\) \(16\)

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

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