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Properties

Label 273.2.bl
Level $273$
Weight $2$
Character orbit 273.bl
Rep. character $\chi_{273}(88,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $38$
Newform subspaces $4$
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.bl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
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 82 38 44
Cusp forms 66 38 28
Eisenstein series 16 0 16

Trace form

\( 38 q - 6 q^{3} + 20 q^{4} - q^{7} + 38 q^{9} + O(q^{10}) \) \( 38 q - 6 q^{3} + 20 q^{4} - q^{7} + 38 q^{9} + 16 q^{10} - 8 q^{12} - 2 q^{13} - 24 q^{14} - 14 q^{16} - 4 q^{17} - 24 q^{20} + 7 q^{21} + 10 q^{22} + 4 q^{23} + 25 q^{25} + 22 q^{26} - 6 q^{27} - 44 q^{28} + 3 q^{31} - 14 q^{35} + 20 q^{36} - 15 q^{37} + 16 q^{38} - 8 q^{39} + 14 q^{40} + 18 q^{41} - 22 q^{42} + 4 q^{43} - 12 q^{44} + 12 q^{46} - 36 q^{47} + 18 q^{48} - 29 q^{49} - 102 q^{50} - 44 q^{52} - 8 q^{53} + 30 q^{55} - 6 q^{56} - 48 q^{59} - 36 q^{60} - 34 q^{61} - 40 q^{62} - q^{63} - 20 q^{64} + 8 q^{65} + 16 q^{66} - 8 q^{68} - 20 q^{69} - 36 q^{70} + 18 q^{71} + 42 q^{73} + 12 q^{74} - 13 q^{75} + 58 q^{77} - 18 q^{78} + 19 q^{79} + 38 q^{81} - 12 q^{82} + 50 q^{84} - 48 q^{85} - 36 q^{86} + 18 q^{87} + 24 q^{88} - 48 q^{89} + 16 q^{90} + 29 q^{91} + 140 q^{92} + 3 q^{93} - 104 q^{94} + 20 q^{95} + 30 q^{96} + 27 q^{97} - 30 q^{98} + O(q^{100}) \)

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.bl.a 273.bl 91.u $2$ $2.180$ \(\Q(\sqrt{-3}) \) None \(3\) \(-2\) \(6\) \(1\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-\zeta_{6})q^{2}-q^{3}+(1-\zeta_{6})q^{4}+(2+\cdots)q^{5}+\cdots\)
273.2.bl.b 273.bl 91.u $4$ $2.180$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(3\) \(4\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{3})q^{2}+q^{3}+(\beta _{1}+\beta _{2}-2\beta _{3})q^{4}+\cdots\)
273.2.bl.c 273.bl 91.u $12$ $2.180$ 12.0.\(\cdots\).1 None \(-3\) \(12\) \(6\) \(3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}-\beta _{6}+\beta _{8})q^{2}+q^{3}+(-1+\cdots)q^{4}+\cdots\)
273.2.bl.d 273.bl 91.u $20$ $2.180$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(-3\) \(-20\) \(-6\) \(-5\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{3}q^{2}-q^{3}+(\beta _{11}+\beta _{17})q^{4}+\beta _{8}q^{5}+\cdots\)

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

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