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Properties

Label 560.2.r
Level $560$
Weight $2$
Character orbit 560.r
Rep. character $\chi_{560}(237,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $184$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 560.r (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 560 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

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

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

Trace form

\( 184 q - 4 q^{2} + 8 q^{8} - 168 q^{9} + O(q^{10}) \) \( 184 q - 4 q^{2} + 8 q^{8} - 168 q^{9} - 8 q^{11} - 8 q^{15} - 8 q^{16} - 4 q^{21} - 12 q^{22} - 32 q^{28} - 44 q^{30} - 24 q^{32} + 20 q^{35} - 40 q^{36} - 8 q^{37} + 48 q^{39} - 32 q^{42} + 24 q^{44} - 8 q^{46} - 4 q^{50} - 8 q^{51} - 4 q^{56} + 24 q^{57} - 4 q^{58} + 64 q^{60} - 32 q^{63} - 8 q^{65} + 12 q^{70} - 64 q^{72} + 40 q^{74} - 28 q^{78} + 104 q^{81} - 48 q^{84} + 16 q^{85} + 8 q^{86} + 96 q^{88} - 20 q^{91} - 56 q^{92} + 16 q^{93} - 56 q^{95} - 80 q^{98} + 24 q^{99} + O(q^{100}) \)

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.r.a 560.r 560.r $184$ $4.472$ None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$