Properties

Label 572.2.bh
Level $572$
Weight $2$
Character orbit 572.bh
Rep. character $\chi_{572}(57,\cdot)$
Character field $\Q(\zeta_{20})$
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.bh (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{20})\)
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

\( 112q - 28q^{9} + O(q^{10}) \) \( 112q - 28q^{9} + 8q^{11} - 10q^{13} + 4q^{15} - 24q^{27} - 20q^{29} - 16q^{31} - 54q^{33} + 100q^{35} - 12q^{37} + 40q^{39} - 20q^{41} - 4q^{45} - 10q^{47} - 76q^{53} - 20q^{55} + 18q^{59} + 40q^{61} + 80q^{63} + 92q^{67} + 8q^{71} - 30q^{73} - 80q^{79} + 12q^{81} + 40q^{85} + 32q^{89} - 12q^{91} - 114q^{93} + 54q^{97} - 90q^{99} + O(q^{100}) \)

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

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

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