Properties

Label 546.2.z
Level $546$
Weight $2$
Character orbit 546.z
Rep. character $\chi_{546}(131,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $2$
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.z (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(224\)
Trace bound: \(11\)
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 64 176
Cusp forms 208 64 144
Eisenstein series 32 0 32

Trace form

\( 64q + 32q^{4} + 4q^{7} + 4q^{9} + O(q^{10}) \) \( 64q + 32q^{4} + 4q^{7} + 4q^{9} + 12q^{10} - 24q^{15} - 32q^{16} - 8q^{21} - 24q^{22} - 12q^{24} - 36q^{25} - 4q^{28} + 2q^{30} - 12q^{31} + 8q^{36} + 12q^{40} - 4q^{42} + 64q^{43} + 32q^{46} - 52q^{49} - 2q^{51} - 16q^{57} - 20q^{58} - 12q^{60} + 72q^{61} + 56q^{63} - 64q^{64} + 48q^{66} - 36q^{70} - 96q^{73} + 12q^{75} + 36q^{79} - 4q^{81} - 16q^{84} - 64q^{85} - 12q^{87} - 12q^{88} - 16q^{91} + 52q^{93} - 12q^{96} + O(q^{100}) \)

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.z.a \(32\) \(4.360\) None \(0\) \(0\) \(0\) \(2\)
546.2.z.b \(32\) \(4.360\) None \(0\) \(0\) \(0\) \(2\)

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

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