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Properties

Label 560.2.cp
Level $560$
Weight $2$
Character orbit 560.cp
Rep. character $\chi_{560}(221,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $256$
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.cp (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(\zeta_{12})\)
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 400 256 144
Cusp forms 368 256 112
Eisenstein series 32 0 32

Trace form

\( 256 q + 4 q^{4} + O(q^{10}) \) \( 256 q + 4 q^{4} + 8 q^{11} + 16 q^{14} - 20 q^{16} - 40 q^{18} - 16 q^{20} + 56 q^{22} - 40 q^{24} + 4 q^{28} - 32 q^{29} - 20 q^{32} + 16 q^{37} - 40 q^{38} - 60 q^{42} + 16 q^{43} + 32 q^{44} - 20 q^{46} + 80 q^{47} - 160 q^{48} - 8 q^{50} - 40 q^{51} + 24 q^{52} - 16 q^{53} - 116 q^{54} - 96 q^{56} - 8 q^{58} + 16 q^{59} - 28 q^{60} + 88 q^{62} - 56 q^{64} - 16 q^{66} - 40 q^{67} - 20 q^{68} - 16 q^{70} + 76 q^{72} + 52 q^{74} - 48 q^{78} + 128 q^{81} - 80 q^{83} - 68 q^{84} + 52 q^{86} + 20 q^{88} - 72 q^{90} - 32 q^{91} - 112 q^{92} + 120 q^{94} + 140 q^{96} + 24 q^{98} - 80 q^{99} + O(q^{100}) \)

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.cp.a 560.cp 112.w $256$ $4.472$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

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

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