Properties

Label 546.2.l
Level $546$
Weight $2$
Character orbit 546.l
Rep. character $\chi_{546}(211,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $32$
Newform subspaces $12$
Sturm bound $224$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.l (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 12 \)
Sturm bound: \(224\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\)

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

\( 32 q - 4 q^{2} - 16 q^{4} - 8 q^{5} + 8 q^{8} - 16 q^{9} + O(q^{10}) \) \( 32 q - 4 q^{2} - 16 q^{4} - 8 q^{5} + 8 q^{8} - 16 q^{9} + 4 q^{10} + 8 q^{11} + 4 q^{13} + 8 q^{15} - 16 q^{16} + 12 q^{17} + 8 q^{18} - 16 q^{19} + 4 q^{20} - 8 q^{22} + 8 q^{23} + 40 q^{25} - 20 q^{26} + 4 q^{29} - 8 q^{30} - 4 q^{32} + 8 q^{33} + 8 q^{34} - 8 q^{35} - 16 q^{36} + 4 q^{37} - 16 q^{38} - 8 q^{39} - 8 q^{40} - 4 q^{41} - 4 q^{42} - 4 q^{43} - 16 q^{44} + 4 q^{45} + 12 q^{46} + 16 q^{47} - 16 q^{49} - 16 q^{50} + 8 q^{51} - 8 q^{52} - 8 q^{53} + 24 q^{55} + 4 q^{58} - 16 q^{60} + 28 q^{61} + 32 q^{64} + 44 q^{65} - 16 q^{66} + 12 q^{67} + 12 q^{68} + 8 q^{69} - 8 q^{71} - 4 q^{72} + 88 q^{73} + 12 q^{74} - 16 q^{76} - 32 q^{77} + 8 q^{78} - 32 q^{79} + 4 q^{80} - 16 q^{81} - 4 q^{82} - 64 q^{83} + 20 q^{85} - 16 q^{86} - 8 q^{88} - 8 q^{90} + 8 q^{91} - 16 q^{92} - 48 q^{95} + 8 q^{97} - 4 q^{98} - 16 q^{99} + O(q^{100}) \)

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.l.a \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(-1\) \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
546.2.l.b \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(6\) \(1\) \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
546.2.l.c \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-4\) \(1\) \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
546.2.l.d \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-4\) \(1\) \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
546.2.l.e \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(-1\) \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
546.2.l.f \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(-4\) \(-1\) \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
546.2.l.g \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(4\) \(1\) \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
546.2.l.h \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(8\) \(-1\) \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
546.2.l.i \(4\) \(4.360\) \(\Q(\sqrt{-3}, \sqrt{17})\) None \(-2\) \(-2\) \(-6\) \(2\) \(q+(-1+\beta _{2})q^{2}+(-1+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)
546.2.l.j \(4\) \(4.360\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(-2\) \(-2\) \(2\) \(-2\) \(q+\beta _{1}q^{2}+\beta _{1}q^{3}+(-1-\beta _{1})q^{4}+\beta _{2}q^{5}+\cdots\)
546.2.l.k \(4\) \(4.360\) \(\Q(\sqrt{-3}, \sqrt{-43})\) None \(-2\) \(2\) \(-8\) \(2\) \(q-\beta _{2}q^{2}+\beta _{2}q^{3}+(-1+\beta _{2})q^{4}-2q^{5}+\cdots\)
546.2.l.l \(4\) \(4.360\) \(\Q(\sqrt{-3}, \sqrt{17})\) None \(-2\) \(2\) \(-2\) \(-2\) \(q+(-1+\beta _{2})q^{2}+(1-\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)