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Properties

Label 221.2.l
Level $221$
Weight $2$
Character orbit 221.l
Rep. character $\chi_{221}(16,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $36$
Newform subspaces $1$
Sturm bound $42$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 221 = 13 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 221.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 221 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(42\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(221, [\chi])\).

Total New Old
Modular forms 44 44 0
Cusp forms 36 36 0
Eisenstein series 8 8 0

Trace form

\( 36 q - 4 q^{2} - 16 q^{4} + 12 q^{8} + 12 q^{9} + O(q^{10}) \) \( 36 q - 4 q^{2} - 16 q^{4} + 12 q^{8} + 12 q^{9} - 14 q^{13} + 2 q^{15} - 4 q^{16} - 2 q^{17} - 24 q^{18} - 6 q^{19} - 44 q^{21} + 30 q^{26} - 6 q^{32} - 20 q^{33} - 64 q^{34} + 36 q^{35} + 26 q^{36} - 16 q^{38} - 16 q^{42} - 16 q^{43} + 20 q^{47} + 8 q^{49} - 28 q^{50} - 8 q^{51} + 102 q^{52} + 48 q^{53} + 36 q^{55} - 2 q^{59} + 88 q^{60} - 12 q^{64} + 24 q^{66} - 46 q^{67} + 10 q^{68} - 2 q^{69} - 4 q^{70} - 82 q^{72} - 22 q^{76} - 28 q^{77} - 2 q^{81} - 40 q^{83} + 24 q^{84} - 24 q^{85} + 104 q^{86} - 34 q^{87} - 46 q^{89} + 28 q^{93} - 22 q^{94} + 68 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(221, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
221.2.l.a 221.l 221.l $36$ $1.765$ None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$