Properties

Label 546.2.k
Level $546$
Weight $2$
Character orbit 546.k
Rep. character $\chi_{546}(373,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $36$
Newform subspaces $5$
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.k (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 5 \)
Sturm bound: \(224\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 240 36 204
Cusp forms 208 36 172
Eisenstein series 32 0 32

Trace form

\( 36q - 4q^{3} - 18q^{4} + 2q^{7} + 36q^{9} + O(q^{10}) \) \( 36q - 4q^{3} - 18q^{4} + 2q^{7} + 36q^{9} - 16q^{10} - 8q^{11} + 2q^{12} + 2q^{13} - 18q^{16} - 4q^{17} - 12q^{19} - 2q^{21} - 4q^{22} + 8q^{23} - 6q^{25} - 4q^{26} - 4q^{27} - 4q^{28} + 4q^{29} + 20q^{31} - 4q^{35} - 18q^{36} - 34q^{37} - 4q^{38} + 18q^{39} + 8q^{40} + 4q^{41} - 6q^{43} + 4q^{44} - 12q^{46} - 24q^{47} + 2q^{48} - 6q^{49} - 16q^{50} - 12q^{51} + 2q^{52} - 12q^{53} + 4q^{55} - 12q^{56} + 20q^{57} + 16q^{58} + 16q^{59} - 52q^{61} + 20q^{62} + 2q^{63} + 36q^{64} + 52q^{65} + 16q^{66} + 32q^{67} - 4q^{68} + 8q^{69} - 64q^{70} + 44q^{71} - 6q^{73} - 12q^{74} + 22q^{75} + 6q^{76} - 28q^{77} - 16q^{78} + 24q^{79} + 36q^{81} - 48q^{82} - 112q^{83} - 8q^{84} - 4q^{86} + 12q^{87} + 8q^{88} + 8q^{89} - 16q^{90} - 56q^{91} - 16q^{92} + 28q^{93} - 80q^{94} + 32q^{95} - 30q^{97} + 24q^{98} - 8q^{99} + O(q^{100}) \)

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.k.a \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-2\) \(0\) \(-5\) \(q-\zeta_{6}q^{2}-q^{3}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{6}+\cdots\)
546.2.k.b \(8\) \(4.360\) 8.0.447703281.1 None \(-4\) \(-8\) \(2\) \(3\) \(q+\beta _{3}q^{2}-q^{3}+(-1-\beta _{3})q^{4}+(1-2\beta _{1}+\cdots)q^{5}+\cdots\)
546.2.k.c \(8\) \(4.360\) 8.0.447703281.1 None \(-4\) \(8\) \(2\) \(-3\) \(q-\beta _{2}q^{2}+q^{3}+(-1+\beta _{2})q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\)
546.2.k.d \(8\) \(4.360\) 8.0.6498455769.2 None \(4\) \(8\) \(-2\) \(3\) \(q+(1-\beta _{4})q^{2}+q^{3}-\beta _{4}q^{4}+\beta _{2}q^{5}+\cdots\)
546.2.k.e \(10\) \(4.360\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(5\) \(-10\) \(-2\) \(4\) \(q+(1+\beta _{5})q^{2}-q^{3}+\beta _{5}q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)

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

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