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Properties

Label 273.2.bt
Level $273$
Weight $2$
Character orbit 273.bt
Rep. character $\chi_{273}(136,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $76$
Newform subspaces $2$
Sturm bound $74$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.bt (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(74\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 164 76 88
Cusp forms 132 76 56
Eisenstein series 32 0 32

Trace form

\( 76 q + 4 q^{7} + 38 q^{9} - 16 q^{11} + 8 q^{12} + 24 q^{14} - 88 q^{16} - 32 q^{19} - 12 q^{21} + 8 q^{22} + 36 q^{24} - 60 q^{26} + 32 q^{28} + 16 q^{29} - 2 q^{31} - 40 q^{32} - 8 q^{35} - 2 q^{37} - 26 q^{39}+ \cdots - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
273.2.bt.a 273.bt 91.aa $36$ $2.180$ None 273.2.bt.a \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{12}]$
273.2.bt.b 273.bt 91.aa $40$ $2.180$ None 273.2.bt.b \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{12}]$

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

\( S_{2}^{\mathrm{old}}(273, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)