Properties

Label 572.2.bf
Level $572$
Weight $2$
Character orbit 572.bf
Rep. character $\chi_{572}(67,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $280$
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.bf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 52 \)
Character field: \(\Q(\zeta_{12})\)
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 352 280 72
Cusp forms 320 280 40
Eisenstein series 32 0 32

Trace form

\( 280q - 4q^{5} + 12q^{6} - 12q^{8} + 140q^{9} + O(q^{10}) \) \( 280q - 4q^{5} + 12q^{6} - 12q^{8} + 140q^{9} - 16q^{14} - 24q^{18} - 16q^{20} + 16q^{21} - 28q^{26} - 40q^{28} - 20q^{32} - 16q^{34} - 36q^{36} - 36q^{37} + 80q^{40} - 40q^{41} + 20q^{42} + 8q^{44} - 40q^{45} + 60q^{46} - 20q^{48} - 144q^{49} + 20q^{50} + 108q^{52} + 8q^{53} + 20q^{54} + 108q^{56} - 64q^{57} + 60q^{58} + 108q^{60} - 20q^{61} - 36q^{62} - 40q^{65} - 40q^{66} - 76q^{68} - 44q^{70} - 20q^{72} - 100q^{73} - 32q^{74} + 32q^{76} - 140q^{78} - 156q^{80} - 140q^{81} - 260q^{84} - 12q^{85} + 56q^{86} - 72q^{88} + 60q^{89} + 80q^{92} + 80q^{93} + 32q^{94} + 80q^{96} + 44q^{97} + 16q^{98} + O(q^{100}) \)

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.bf.a \(280\) \(4.567\) None \(0\) \(0\) \(-4\) \(0\)

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

\( S_{2}^{\mathrm{old}}(572, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 2}\)