Properties

Label 572.2.bm
Level $572$
Weight $2$
Character orbit 572.bm
Rep. character $\chi_{572}(35,\cdot)$
Character field $\Q(\zeta_{30})$
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.bm (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 572 \)
Character field: \(\Q(\zeta_{30})\)
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

\( 640q - 5q^{2} - 3q^{4} - 24q^{5} - 5q^{6} - 20q^{8} - 78q^{9} + O(q^{10}) \) \( 640q - 5q^{2} - 3q^{4} - 24q^{5} - 5q^{6} - 20q^{8} - 78q^{9} - 36q^{12} - 20q^{13} - 28q^{14} - 11q^{16} - 10q^{17} - 20q^{18} - 29q^{20} + 25q^{22} - 65q^{24} - 152q^{25} + 40q^{26} - 5q^{28} - 10q^{29} + 5q^{30} + 4q^{33} - 132q^{34} - 24q^{36} - 6q^{37} - 10q^{38} - 20q^{40} - 50q^{41} - 49q^{42} - 4q^{44} + 28q^{45} - 25q^{46} + 35q^{48} + 62q^{49} + 20q^{50} + 15q^{52} - 8q^{53} - 2q^{56} - 40q^{57} + 41q^{58} - 68q^{60} - 10q^{61} - 5q^{62} - 36q^{64} - 66q^{66} + 60q^{68} - 58q^{69} + 118q^{70} - 5q^{72} - 40q^{73} + 45q^{74} - 76q^{77} + 12q^{78} - 41q^{80} + 30q^{81} - 37q^{82} + 50q^{84} - 10q^{85} - 120q^{86} + 89q^{88} - 40q^{89} - 250q^{90} - 46q^{92} - 2q^{93} - 5q^{94} + 110q^{96} - 10q^{97} + O(q^{100}) \)

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.bm.a \(640\) \(4.567\) None \(-5\) \(0\) \(-24\) \(0\)