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Properties

Label 273.2.bd
Level $273$
Weight $2$
Character orbit 273.bd
Rep. character $\chi_{273}(43,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $2$
Sturm bound $74$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.bd (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(74\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(273, [\chi])\).

Total New Old
Modular forms 84 32 52
Cusp forms 68 32 36
Eisenstein series 16 0 16

Trace form

\( 32 q + 20 q^{4} - 16 q^{9} + O(q^{10}) \) \( 32 q + 20 q^{4} - 16 q^{9} - 8 q^{10} - 12 q^{11} + 16 q^{12} - 8 q^{13} - 12 q^{15} - 20 q^{16} + 8 q^{17} + 24 q^{20} - 20 q^{22} - 8 q^{23} - 8 q^{25} + 40 q^{26} + 12 q^{33} + 4 q^{35} + 20 q^{36} + 12 q^{37} - 56 q^{38} - 8 q^{39} - 88 q^{40} - 12 q^{41} - 4 q^{42} + 4 q^{43} - 12 q^{45} - 12 q^{46} + 16 q^{49} + 60 q^{50} - 24 q^{51} + 4 q^{52} + 40 q^{53} + 12 q^{55} + 12 q^{58} - 84 q^{59} - 4 q^{61} - 4 q^{62} - 32 q^{64} - 64 q^{65} - 32 q^{66} + 12 q^{67} + 16 q^{68} + 4 q^{69} + 24 q^{74} - 16 q^{75} + 48 q^{76} + 16 q^{77} + 24 q^{78} + 88 q^{79} + 144 q^{80} - 16 q^{81} - 60 q^{82} + 24 q^{85} + 24 q^{87} + 60 q^{88} + 96 q^{89} + 16 q^{90} - 8 q^{91} - 136 q^{92} - 8 q^{94} - 28 q^{95} - 60 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(273, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
273.2.bd.a 273.bd 13.e $16$ $2.180$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{2}q^{2}+(-1+\beta _{12})q^{3}+(1+\beta _{3}+\cdots)q^{4}+\cdots\)
273.2.bd.b 273.bd 13.e $16$ $2.180$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{14}q^{2}-\beta _{5}q^{3}+(2+2\beta _{5}+\beta _{7}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(273, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(273, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)