Properties

Label 561.2.bf
Level $561$
Weight $2$
Character orbit 561.bf
Rep. character $\chi_{561}(140,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $544$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 561 = 3 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 561.bf (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 561 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(561, [\chi])\).

Total New Old
Modular forms 608 608 0
Cusp forms 544 544 0
Eisenstein series 64 64 0

Trace form

\( 544 q - 2 q^{3} + 104 q^{4} - 20 q^{6} - 20 q^{7} + O(q^{10}) \) \( 544 q - 2 q^{3} + 104 q^{4} - 20 q^{6} - 20 q^{7} - 24 q^{12} - 40 q^{13} - 168 q^{16} - 20 q^{18} + 44 q^{22} - 60 q^{24} + 16 q^{27} - 20 q^{28} - 20 q^{30} - 40 q^{31} - 44 q^{33} + 24 q^{34} + 24 q^{37} - 90 q^{39} + 60 q^{40} + 4 q^{45} - 100 q^{46} - 22 q^{48} - 90 q^{51} + 40 q^{52} - 4 q^{55} + 20 q^{57} - 84 q^{58} - 60 q^{61} + 20 q^{63} + 240 q^{64} - 64 q^{67} - 60 q^{69} - 140 q^{72} - 20 q^{73} - 40 q^{75} - 24 q^{78} + 20 q^{79} + 92 q^{81} - 120 q^{82} + 180 q^{84} - 220 q^{85} - 84 q^{88} - 120 q^{90} - 212 q^{91} - 60 q^{96} + 152 q^{97} - 34 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(561, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
561.2.bf.a 561.bf 561.af $544$ $4.480$ None \(0\) \(-2\) \(0\) \(-20\) $\mathrm{SU}(2)[C_{20}]$