Properties

Label 572.2.bv
Level $572$
Weight $2$
Character orbit 572.bv
Rep. character $\chi_{572}(41,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $224$
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.bv (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
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 1440 224 1216
Cusp forms 1248 224 1024
Eisenstein series 192 0 192

Trace form

\( 224q + 28q^{9} + O(q^{10}) \) \( 224q + 28q^{9} + 16q^{11} + 10q^{13} - 28q^{15} - 48q^{23} + 24q^{27} + 20q^{29} + 4q^{31} + 60q^{33} + 50q^{35} + 12q^{37} - 40q^{39} + 20q^{41} + 64q^{45} - 62q^{47} + 100q^{53} - 22q^{55} + 12q^{59} - 40q^{61} - 80q^{63} - 44q^{67} - 152q^{71} + 30q^{73} - 120q^{75} + 80q^{79} + 72q^{81} + 90q^{83} - 40q^{85} - 8q^{89} - 36q^{91} - 90q^{93} - 42q^{97} + 144q^{99} + O(q^{100}) \)

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.bv.a \(224\) \(4.567\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(572, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(286, [\chi])\)\(^{\oplus 2}\)