Properties

Label 546.2.bi
Level $546$
Weight $2$
Character orbit 546.bi
Rep. character $\chi_{546}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $76$
Newform subspaces $6$
Sturm bound $224$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bi (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: \(5\)
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

\( 76q + 76q^{4} - 2q^{7} - 4q^{9} + O(q^{10}) \) \( 76q + 76q^{4} - 2q^{7} - 4q^{9} + 2q^{13} - 12q^{15} + 76q^{16} + 24q^{18} - 14q^{19} + 42q^{25} - 2q^{28} + 2q^{30} - 16q^{31} + 12q^{33} - 4q^{36} + 18q^{39} - 14q^{42} - 10q^{43} - 26q^{49} + 6q^{51} + 2q^{52} - 36q^{54} - 24q^{55} - 12q^{60} - 78q^{61} + 18q^{63} + 76q^{64} + 24q^{66} - 60q^{67} + 54q^{69} + 24q^{72} + 2q^{73} - 14q^{76} + 4q^{78} - 4q^{79} - 4q^{81} - 24q^{82} - 48q^{85} - 80q^{91} - 72q^{94} - 14q^{97} + O(q^{100}) \)

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

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

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