Properties

Label 572.2.bk
Level $572$
Weight $2$
Character orbit 572.bk
Rep. character $\chi_{572}(31,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $640$
Newform subspaces $1$
Sturm bound $168$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 572.bk (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 572 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(168\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(572, [\chi])\).

Total New Old
Modular forms 704 704 0
Cusp forms 640 640 0
Eisenstein series 64 64 0

Trace form

\( 640q - 6q^{2} - 12q^{5} - 14q^{6} - 6q^{8} + 120q^{9} + O(q^{10}) \) \( 640q - 6q^{2} - 12q^{5} - 14q^{6} - 6q^{8} + 120q^{9} - 12q^{13} + 4q^{14} - 36q^{16} - 10q^{18} - 60q^{20} - 56q^{21} - 44q^{22} - 14q^{24} + 26q^{26} - 14q^{28} - 24q^{29} - 16q^{32} - 28q^{33} + 12q^{34} - 12q^{37} + 4q^{40} - 36q^{41} - 8q^{42} + 26q^{44} - 16q^{45} - 50q^{46} + 48q^{48} + 36q^{50} - 52q^{52} - 40q^{53} + 116q^{54} - 36q^{57} - 70q^{58} + 52q^{60} - 8q^{61} - 48q^{65} - 228q^{66} - 44q^{68} - 68q^{70} - 38q^{72} - 12q^{73} - 12q^{74} + 108q^{76} + 108q^{78} + 62q^{80} - 168q^{81} - 36q^{84} - 52q^{85} - 62q^{86} + 16q^{89} - 80q^{92} - 4q^{93} - 124q^{94} - 132q^{96} - 4q^{97} - 108q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(572, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
572.2.bk.a \(640\) \(4.567\) None \(-6\) \(0\) \(-12\) \(0\)