Properties

Label 546.2.bk
Level $546$
Weight $2$
Character orbit 546.bk
Rep. character $\chi_{546}(25,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $40$
Newform subspaces $3$
Sturm bound $224$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bk (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(224\)
Trace bound: \(1\)
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 40 200
Cusp forms 208 40 168
Eisenstein series 32 0 32

Trace form

\( 40q + 20q^{4} - 20q^{9} + O(q^{10}) \) \( 40q + 20q^{4} - 20q^{9} + 8q^{10} - 4q^{14} - 20q^{16} + 4q^{17} + 8q^{22} - 8q^{23} + 20q^{25} + 4q^{26} - 8q^{29} + 56q^{35} - 40q^{36} + 4q^{38} + 4q^{39} - 8q^{40} + 36q^{49} + 16q^{51} - 28q^{53} + 64q^{55} - 20q^{56} - 4q^{61} + 64q^{62} - 40q^{64} - 4q^{65} - 16q^{66} - 4q^{68} - 48q^{69} + 24q^{74} + 16q^{75} - 32q^{77} - 24q^{78} - 8q^{79} - 20q^{81} - 24q^{87} + 4q^{88} - 16q^{90} + 52q^{91} - 16q^{92} - 28q^{94} - 48q^{95} + O(q^{100}) \)

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.bk.a \(8\) \(4.360\) 8.0.3317760000.2 None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{2}q^{2}-\beta _{4}q^{3}+\beta _{4}q^{4}+(\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
546.2.bk.b \(12\) \(4.360\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-6\) \(0\) \(0\) \(q-\beta _{6}q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+\beta _{8}q^{5}+\cdots\)
546.2.bk.c \(20\) \(4.360\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(10\) \(0\) \(0\) \(q+\beta _{8}q^{2}+\beta _{3}q^{3}+\beta _{3}q^{4}-\beta _{9}q^{5}+\cdots\)

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

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