Properties

Label 572.2.bn
Level $572$
Weight $2$
Character orbit 572.bn
Rep. character $\chi_{572}(95,\cdot)$
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.bn (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

\( 640q - 15q^{2} - 3q^{4} - 15q^{6} - 78q^{9} + O(q^{10}) \) \( 640q - 15q^{2} - 3q^{4} - 15q^{6} - 78q^{9} - 4q^{12} - 20q^{13} - 12q^{14} - 19q^{16} - 10q^{17} - 45q^{20} - 15q^{22} - 15q^{24} + 104q^{25} - 20q^{26} - 15q^{28} - 10q^{29} + 45q^{30} - 24q^{33} + 4q^{36} - 18q^{37} - 14q^{38} - 20q^{40} - 30q^{41} - 13q^{42} - 108q^{45} - 15q^{46} + 35q^{48} - 74q^{49} - 90q^{50} + 15q^{52} - 8q^{53} + 50q^{56} + 27q^{58} - 10q^{61} - 5q^{62} - 84q^{64} - 146q^{66} - 70q^{68} - 26q^{69} - 15q^{72} - 55q^{74} + 44q^{77} + 24q^{78} - 39q^{80} + 30q^{81} - 29q^{82} + 30q^{84} - 30q^{85} - 75q^{88} - 24q^{89} + 30q^{90} + 14q^{92} + 66q^{93} - 5q^{94} - 30q^{97} + O(q^{100}) \)

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.bn.a \(640\) \(4.567\) None \(-15\) \(0\) \(0\) \(0\)