Properties

Label 572.2.y
Level $572$
Weight $2$
Character orbit 572.y
Rep. character $\chi_{572}(79,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $288$
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.y (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 44 \)
Character field: \(\Q(\zeta_{10})\)
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 352 288 64
Cusp forms 320 288 32
Eisenstein series 32 0 32

Trace form

\( 288q - 4q^{4} + 80q^{9} + O(q^{10}) \) \( 288q - 4q^{4} + 80q^{9} + 8q^{12} - 6q^{14} - 32q^{16} - 50q^{18} + 16q^{22} - 88q^{25} - 50q^{28} - 20q^{30} - 4q^{33} + 30q^{36} - 48q^{37} + 38q^{38} + 70q^{40} + 56q^{42} + 66q^{44} - 96q^{45} + 70q^{46} + 76q^{48} - 56q^{49} + 70q^{50} - 20q^{52} - 80q^{53} + 44q^{56} - 20q^{57} - 2q^{58} - 144q^{60} - 150q^{62} - 100q^{64} + 30q^{66} + 24q^{69} - 28q^{70} - 100q^{72} + 40q^{73} - 140q^{74} - 24q^{77} - 40q^{78} + 118q^{80} - 76q^{81} + 56q^{82} + 120q^{84} + 80q^{85} + 44q^{88} - 8q^{89} + 80q^{90} - 14q^{92} + 72q^{93} + 50q^{94} - 140q^{96} + 116q^{97} + O(q^{100}) \)

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.y.a \(288\) \(4.567\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(572, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(572, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 2}\)