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Properties

Label 273.2.cd
Level $273$
Weight $2$
Character orbit 273.cd
Rep. character $\chi_{273}(44,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $136$
Newform subspaces $5$
Sturm bound $74$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.cd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 5 \)
Sturm bound: \(74\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(5\), \(19\)

Dimensions

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

Total New Old
Modular forms 168 168 0
Cusp forms 136 136 0
Eisenstein series 32 32 0

Trace form

\( 136 q - 4 q^{3} - 16 q^{6} - 2 q^{7} - 4 q^{9} + O(q^{10}) \) \( 136 q - 4 q^{3} - 16 q^{6} - 2 q^{7} - 4 q^{9} - 16 q^{13} - 12 q^{15} + 48 q^{16} - 26 q^{18} - 6 q^{19} - 6 q^{21} - 32 q^{22} + 20 q^{24} - 40 q^{27} - 36 q^{28} - 14 q^{31} - 16 q^{33} + 48 q^{34} - 6 q^{37} - 32 q^{39} - 112 q^{40} - 40 q^{42} - 2 q^{45} + 24 q^{46} + 56 q^{48} - 16 q^{52} + 14 q^{54} - 16 q^{55} - 44 q^{57} - 28 q^{58} + 44 q^{60} + 8 q^{61} + 32 q^{63} - 4 q^{66} - 2 q^{67} - 44 q^{70} - 26 q^{72} - 38 q^{73} - 8 q^{76} + 40 q^{78} + 48 q^{79} + 36 q^{81} - 158 q^{84} + 80 q^{85} - 56 q^{87} + 26 q^{91} + 4 q^{93} + 32 q^{94} - 126 q^{96} - 4 q^{99} + O(q^{100}) \)

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.cd.a 273.cd 273.bd $4$ $2.180$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{12}]$ \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(2\zeta_{12}-2\zeta_{12}^{3})q^{4}+\cdots\)
273.2.cd.b 273.cd 273.bd $4$ $2.180$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(2\) $\mathrm{U}(1)[D_{12}]$ \(q+(\zeta_{12}+\zeta_{12}^{3})q^{3}+(2\zeta_{12}-2\zeta_{12}^{3})q^{4}+\cdots\)
273.2.cd.c 273.cd 273.bd $8$ $2.180$ \(\Q(\zeta_{24})\) None \(0\) \(4\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+\zeta_{24}^{7}q^{2}+(1-\zeta_{24}^{2}+\zeta_{24}^{3}-\zeta_{24}^{4}+\cdots)q^{3}+\cdots\)
273.2.cd.d 273.cd 273.bd $8$ $2.180$ \(\Q(\zeta_{24})\) None \(0\) \(4\) \(4\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+\zeta_{24}^{7}q^{2}+(1+\zeta_{24}^{2}-\zeta_{24}^{4}+\zeta_{24}^{5}+\cdots)q^{3}+\cdots\)
273.2.cd.e 273.cd 273.bd $112$ $2.180$ None \(0\) \(-12\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{12}]$