Properties

Label 546.2.i
Level $546$
Weight $2$
Character orbit 546.i
Rep. character $\chi_{546}(79,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $32$
Newform subspaces $11$
Sturm bound $224$
Trace bound $5$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 240 32 208
Cusp forms 208 32 176
Eisenstein series 32 0 32

Trace form

\( 32q - 16q^{4} + 8q^{5} + 8q^{6} - 12q^{7} - 16q^{9} + O(q^{10}) \) \( 32q - 16q^{4} + 8q^{5} + 8q^{6} - 12q^{7} - 16q^{9} + 4q^{10} + 8q^{11} + 8q^{13} - 4q^{14} - 8q^{15} - 16q^{16} - 12q^{17} - 8q^{19} - 16q^{20} - 4q^{24} - 20q^{25} + 12q^{28} - 24q^{29} - 8q^{30} + 20q^{31} - 4q^{33} + 16q^{34} - 24q^{35} + 32q^{36} + 20q^{38} + 4q^{40} + 64q^{41} + 12q^{42} - 32q^{43} + 8q^{44} + 8q^{45} - 8q^{46} + 24q^{47} - 16q^{49} - 32q^{50} + 8q^{51} - 4q^{52} + 12q^{53} - 4q^{54} + 8q^{55} - 4q^{56} + 16q^{57} + 12q^{58} + 4q^{60} - 4q^{61} + 16q^{62} + 32q^{64} - 8q^{65} + 16q^{67} - 12q^{68} - 32q^{69} - 12q^{70} - 16q^{73} + 16q^{76} - 8q^{77} + 12q^{79} + 8q^{80} - 16q^{81} - 32q^{85} - 16q^{86} + 4q^{87} - 16q^{89} - 8q^{90} + 16q^{91} - 8q^{93} + 4q^{94} - 24q^{95} - 4q^{96} - 40q^{97} - 48q^{98} - 16q^{99} + O(q^{100}) \)

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.i.a \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(-3\) \(-1\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.b \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(-1\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.c \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(4\) \(-1\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.d \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(-5\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.e \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(2\) \(-5\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.f \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(-1\) \(-1\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.g \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(2\) \(-1\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.h \(4\) \(4.360\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(-2\) \(0\) \(2\) \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+\beta _{1}q^{5}+\cdots\)
546.2.i.i \(4\) \(4.360\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(2\) \(4\) \(-2\) \(q+\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots\)
546.2.i.j \(4\) \(4.360\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(2\) \(-2\) \(2\) \(0\) \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
546.2.i.k \(6\) \(4.360\) 6.0.21870000.1 None \(3\) \(3\) \(-3\) \(3\) \(q+(1+\beta _{2})q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)