Properties

Label 546.2.bn
Level $546$
Weight $2$
Character orbit 546.bn
Rep. character $\chi_{546}(101,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $76$
Newform subspaces $6$
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.bn (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
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 76 164
Cusp forms 208 76 132
Eisenstein series 32 0 32

Trace form

\( 76q - 38q^{4} + 2q^{7} + 8q^{9} + O(q^{10}) \) \( 76q - 38q^{4} + 2q^{7} + 8q^{9} - 2q^{13} - 12q^{15} - 38q^{16} - 24q^{18} - 28q^{19} + 42q^{25} - 4q^{28} - 4q^{30} + 16q^{31} + 24q^{33} - 4q^{36} + 42q^{37} + 12q^{39} + 16q^{42} - 10q^{43} - 12q^{46} - 14q^{49} + 6q^{51} - 14q^{52} - 18q^{54} + 24q^{55} + 12q^{60} + 12q^{63} + 76q^{64} + 24q^{66} - 54q^{69} - 2q^{73} - 108q^{75} + 14q^{76} + 4q^{78} - 4q^{79} + 8q^{81} - 48q^{85} - 24q^{87} - 32q^{91} - 12q^{93} + 14q^{97} + O(q^{100}) \)

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.bn.a \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(-3\) \(1\) \(q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.bn.b \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-6\) \(-5\) \(q-\zeta_{6}q^{2}+(-1+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.bn.c \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(6\) \(-5\) \(q+\zeta_{6}q^{2}+(-1+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.bn.d \(2\) \(4.360\) \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(3\) \(1\) \(q+\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.bn.e \(34\) \(4.360\) None \(-17\) \(3\) \(9\) \(5\)
546.2.bn.f \(34\) \(4.360\) None \(17\) \(-3\) \(-9\) \(5\)

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

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