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Properties

Label 561.2.bi
Level $561$
Weight $2$
Character orbit 561.bi
Rep. character $\chi_{561}(25,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $576$
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.bi (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 187 \)
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 576 640
Cusp forms 1088 576 512
Eisenstein series 128 0 128

Trace form

\( 576 q + 16 q^{5} + O(q^{10}) \) \( 576 q + 16 q^{5} - 8 q^{11} + 144 q^{16} - 48 q^{17} - 112 q^{22} - 16 q^{23} - 16 q^{25} - 32 q^{26} + 16 q^{28} - 56 q^{31} - 80 q^{32} + 8 q^{33} + 32 q^{34} + 16 q^{37} - 32 q^{39} - 168 q^{40} - 32 q^{42} - 16 q^{43} + 32 q^{44} + 32 q^{46} - 24 q^{49} + 192 q^{52} + 16 q^{53} - 48 q^{57} - 192 q^{58} - 64 q^{59} - 136 q^{61} + 80 q^{62} + 64 q^{65} - 64 q^{66} - 176 q^{68} + 24 q^{69} - 176 q^{70} + 64 q^{71} - 16 q^{73} - 32 q^{75} - 256 q^{76} + 240 q^{77} + 48 q^{78} - 32 q^{79} - 72 q^{80} + 96 q^{82} - 16 q^{83} - 56 q^{85} + 8 q^{88} - 32 q^{91} - 80 q^{92} - 144 q^{93} - 24 q^{94} + 40 q^{95} + 96 q^{96} - 32 q^{97} - 8 q^{99} + O(q^{100}) \)

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.bi.a 561.bi 187.r $576$ $4.480$ None \(0\) \(0\) \(16\) \(0\) $\mathrm{SU}(2)[C_{40}]$

Decomposition of \(S_{2}^{\mathrm{old}}(561, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(561, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(187, [\chi])\)\(^{\oplus 2}\)