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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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(546, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
546.2.bi.a 546.bi 273.ar $2$ $4.360$ \(\Q(\sqrt{-3}) \) None \(-2\) \(-3\) \(6\) \(-1\) $\mathrm{SU}(2)[C_{6}]$ \(q-q^{2}+(-2+\zeta_{6})q^{3}+q^{4}+(4-2\zeta_{6})q^{5}+\cdots\)
546.2.bi.b 546.bi 273.ar $2$ $4.360$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(3\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q-q^{2}+(-1+2\zeta_{6})q^{3}+q^{4}+(2-\zeta_{6})q^{5}+\cdots\)
546.2.bi.c 546.bi 273.ar $2$ $4.360$ \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(-6\) \(-1\) $\mathrm{SU}(2)[C_{6}]$ \(q+q^{2}+(-2+\zeta_{6})q^{3}+q^{4}+(-4+2\zeta_{6})q^{5}+\cdots\)
546.2.bi.d 546.bi 273.ar $2$ $4.360$ \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(-3\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q+q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(-2+\zeta_{6})q^{5}+\cdots\)
546.2.bi.e 546.bi 273.ar $34$ $4.360$ None \(-34\) \(3\) \(-9\) \(4\) $\mathrm{SU}(2)[C_{6}]$
546.2.bi.f 546.bi 273.ar $34$ $4.360$ None \(34\) \(6\) \(9\) \(4\) $\mathrm{SU}(2)[C_{6}]$

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

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