Properties

Label 546.2.q
Level $546$
Weight $2$
Character orbit 546.q
Rep. character $\chi_{546}(251,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $72$
Newform subspaces $10$
Sturm bound $224$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 10 \)
Sturm bound: \(224\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\), \(11\), \(17\)

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

\( 72q - 36q^{4} - 4q^{9} + O(q^{10}) \) \( 72q - 36q^{4} - 4q^{9} - 12q^{15} - 36q^{16} - 56q^{25} - 16q^{30} - 4q^{36} + 48q^{39} + 16q^{42} - 20q^{43} + 12q^{46} - 12q^{49} - 48q^{51} + 96q^{63} + 72q^{64} - 84q^{67} + 12q^{72} - 44q^{78} + 16q^{79} + 56q^{81} - 120q^{85} + 32q^{91} + 48q^{93} + O(q^{100}) \)

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.q.a \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(0\) \(1\) \(q+(-1+\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
546.2.q.b \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(0\) \(5\) \(q+(-1+\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
546.2.q.c \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(0\) \(1\) \(q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
546.2.q.d \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(0\) \(5\) \(q+(1-\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
546.2.q.e \(4\) \(4.360\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-2\) \(-1\) \(0\) \(2\) \(q-\beta _{2}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
546.2.q.f \(4\) \(4.360\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-2\) \(1\) \(0\) \(10\) \(q+(-1+\beta _{2})q^{2}+(\beta _{2}+\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
546.2.q.g \(4\) \(4.360\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(2\) \(-2\) \(0\) \(2\) \(q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
546.2.q.h \(4\) \(4.360\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(2\) \(2\) \(0\) \(10\) \(q+\beta _{2}q^{2}+(1-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
546.2.q.i \(24\) \(4.360\) None \(-12\) \(0\) \(0\) \(-18\)
546.2.q.j \(24\) \(4.360\) None \(12\) \(0\) \(0\) \(-18\)

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

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