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Properties

Label 561.2.bg
Level $561$
Weight $2$
Character orbit 561.bg
Rep. character $\chi_{561}(2,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $1088$
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.bg (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 561 \)
Character field: \(\Q(\zeta_{40})\)
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 1216 1216 0
Cusp forms 1088 1088 0
Eisenstein series 128 128 0

Trace form

\( 1088 q - 12 q^{3} - 20 q^{6} - 40 q^{7} - 36 q^{9} + O(q^{10}) \) \( 1088 q - 12 q^{3} - 20 q^{6} - 40 q^{7} - 36 q^{9} - 80 q^{12} - 36 q^{15} + 176 q^{16} - 40 q^{18} - 40 q^{19} - 128 q^{22} - 80 q^{24} - 24 q^{25} - 12 q^{27} - 40 q^{28} - 32 q^{31} - 48 q^{33} - 96 q^{34} + 56 q^{36} - 40 q^{37} - 20 q^{39} - 200 q^{40} + 12 q^{42} - 32 q^{45} - 40 q^{46} + 60 q^{48} - 152 q^{49} - 20 q^{51} + 80 q^{52} - 80 q^{57} + 88 q^{58} - 124 q^{60} - 40 q^{61} + 40 q^{63} - 152 q^{66} - 64 q^{67} - 120 q^{69} - 56 q^{70} - 40 q^{73} + 72 q^{75} - 112 q^{78} - 40 q^{79} + 144 q^{82} - 440 q^{84} + 120 q^{85} - 8 q^{88} - 20 q^{90} - 88 q^{91} - 44 q^{93} + 200 q^{94} - 20 q^{96} - 208 q^{97} + 108 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.bg.a 561.bg 561.ag $1088$ $4.480$ None \(0\) \(-12\) \(0\) \(-40\) $\mathrm{SU}(2)[C_{40}]$