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Properties

Label 560.2.cq
Level $560$
Weight $2$
Character orbit 560.cq
Rep. character $\chi_{560}(131,\cdot)$
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.cq (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

\( 256 q + 4 q^{4} + O(q^{10}) \) \( 256 q + 4 q^{4} - 8 q^{11} - 16 q^{14} - 20 q^{16} + 40 q^{18} + 40 q^{22} + 16 q^{23} - 44 q^{28} + 32 q^{29} + 20 q^{32} - 16 q^{37} - 60 q^{42} - 16 q^{43} - 48 q^{44} - 20 q^{46} - 8 q^{50} + 40 q^{51} - 72 q^{52} - 16 q^{53} - 84 q^{54} - 96 q^{56} - 8 q^{58} - 48 q^{59} - 28 q^{60} + 40 q^{64} - 192 q^{66} - 40 q^{67} - 60 q^{68} - 16 q^{70} + 64 q^{71} + 36 q^{72} - 60 q^{74} + 48 q^{78} + 128 q^{81} + 164 q^{84} - 52 q^{86} - 20 q^{88} + 32 q^{91} + 128 q^{92} + 72 q^{94} - 204 q^{96} + 160 q^{98} - 80 q^{99} + O(q^{100}) \)

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

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

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