Properties

Label 572.2.s
Level $572$
Weight $2$
Character orbit 572.s
Rep. character $\chi_{572}(43,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $160$
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.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 572 \)
Character field: \(\Q(\zeta_{6})\)
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 176 176 0
Cusp forms 160 160 0
Eisenstein series 16 16 0

Trace form

\( 160q - 2q^{4} + 68q^{9} + O(q^{10}) \) \( 160q - 2q^{4} + 68q^{9} - 36q^{12} - 8q^{14} - 6q^{16} + 30q^{20} - 20q^{22} - 144q^{25} - 40q^{26} - 6q^{33} + 46q^{36} - 12q^{37} - 56q^{38} - 2q^{42} + 48q^{45} - 40q^{48} + 44q^{49} - 32q^{53} + 30q^{56} + 78q^{58} + 64q^{64} - 4q^{66} - 44q^{69} - 44q^{77} + 16q^{78} + 24q^{80} - 40q^{81} - 6q^{82} - 10q^{88} + 24q^{89} - 24q^{92} - 96q^{93} + O(q^{100}) \)

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.s.a \(160\) \(4.567\) None \(0\) \(0\) \(0\) \(0\)