Properties

Label 572.2.bs
Level $572$
Weight $2$
Character orbit 572.bs
Rep. character $\chi_{572}(15,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $1280$
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.bs (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 572 \)
Character field: \(\Q(\zeta_{60})\)
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 1408 1408 0
Cusp forms 1280 1280 0
Eisenstein series 128 128 0

Trace form

\( 1280q - 12q^{2} - 18q^{4} - 24q^{5} - 4q^{6} - 12q^{8} - 156q^{9} + O(q^{10}) \) \( 1280q - 12q^{2} - 18q^{4} - 24q^{5} - 4q^{6} - 12q^{8} - 156q^{9} - 48q^{10} - 24q^{13} - 40q^{14} + 18q^{16} - 36q^{17} - 8q^{18} + 18q^{20} - 40q^{21} - 10q^{22} - 100q^{24} - 44q^{26} - 4q^{28} - 12q^{29} - 114q^{30} - 92q^{32} - 20q^{33} + 36q^{34} - 72q^{36} - 24q^{37} + 8q^{40} + 26q^{42} - 20q^{44} - 80q^{45} + 32q^{46} + 30q^{48} - 36q^{49} - 78q^{50} + 34q^{52} - 80q^{53} - 188q^{54} - 48q^{56} - 92q^{58} + 20q^{60} - 28q^{61} + 42q^{62} - 48q^{65} + 204q^{66} + 26q^{68} - 36q^{69} + 38q^{70} - 136q^{72} - 24q^{73} - 6q^{74} - 276q^{76} - 156q^{78} - 80q^{80} + 60q^{81} + 162q^{82} - 108q^{84} + 16q^{85} - 88q^{86} + 6q^{88} - 64q^{89} - 16q^{92} + 64q^{93} + 34q^{94} + 114q^{96} - 8q^{97} - 24q^{98} + O(q^{100}) \)

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.bs.a \(1280\) \(4.567\) None \(-12\) \(0\) \(-24\) \(0\)