Properties

Label 572.2.bg
Level $572$
Weight $2$
Character orbit 572.bg
Rep. character $\chi_{572}(9,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $112$
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.bg (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{15})\)
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 720 112 608
Cusp forms 624 112 512
Eisenstein series 96 0 96

Trace form

\( 112q + 8q^{9} + O(q^{10}) \) \( 112q + 8q^{9} - 10q^{11} + 11q^{13} - 2q^{15} + 4q^{17} - 12q^{19} - 40q^{21} + 10q^{23} - 16q^{25} - 12q^{27} + q^{29} + 4q^{31} + 35q^{33} - 5q^{35} - 12q^{37} + 21q^{39} - 10q^{41} - 32q^{43} + 34q^{45} + 70q^{47} + 16q^{49} - 48q^{51} - 26q^{53} + 10q^{55} - 12q^{57} - 5q^{59} + 28q^{61} + 34q^{63} + 22q^{65} - 68q^{67} - 58q^{69} + 44q^{71} + 42q^{73} - 24q^{75} + 46q^{77} - 24q^{79} + 64q^{81} - 114q^{83} + 4q^{85} - 30q^{87} - 6q^{89} + 77q^{91} - 5q^{93} - 36q^{95} - 15q^{97} - 40q^{99} + O(q^{100}) \)

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.bg.a \(112\) \(4.567\) None \(0\) \(0\) \(0\) \(0\)

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

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