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Properties

Label 560.2.bd
Level $560$
Weight $2$
Character orbit 560.bd
Rep. character $\chi_{560}(141,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $96$
Newform subspaces $2$
Sturm bound $192$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 560.bd (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(560, [\chi])\).

Total New Old
Modular forms 200 96 104
Cusp forms 184 96 88
Eisenstein series 16 0 16

Trace form

\( 96 q + 4 q^{4} + 24 q^{6} + O(q^{10}) \) \( 96 q + 4 q^{4} + 24 q^{6} - 8 q^{10} + 8 q^{11} + 24 q^{12} + 4 q^{14} + 16 q^{15} - 12 q^{16} - 20 q^{18} + 16 q^{19} - 4 q^{22} + 24 q^{24} + 32 q^{26} - 48 q^{27} + 16 q^{29} - 40 q^{32} - 32 q^{34} + 8 q^{36} + 16 q^{37} - 8 q^{43} - 4 q^{44} - 32 q^{46} - 96 q^{49} + 4 q^{50} - 16 q^{51} - 64 q^{52} - 16 q^{53} - 32 q^{54} - 4 q^{56} - 52 q^{58} + 48 q^{59} - 32 q^{61} - 72 q^{62} - 40 q^{63} + 76 q^{64} - 32 q^{66} - 40 q^{67} + 56 q^{68} - 32 q^{69} + 4 q^{72} + 92 q^{74} - 16 q^{77} + 80 q^{78} - 32 q^{79} - 32 q^{80} - 96 q^{81} + 152 q^{82} + 32 q^{85} - 132 q^{86} - 20 q^{88} + 48 q^{92} + 96 q^{93} + 24 q^{94} - 64 q^{95} + 48 q^{96} - 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(560, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
560.2.bd.a 560.bd 16.e $44$ $4.472$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
560.2.bd.b 560.bd 16.e $52$ $4.472$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(560, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(560, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)