Properties

Label 572.2.m
Level $572$
Weight $2$
Character orbit 572.m
Rep. character $\chi_{572}(21,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $28$
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.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(i)\)
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 180 28 152
Cusp forms 156 28 128
Eisenstein series 24 0 24

Trace form

\( 28q + 28q^{9} + O(q^{10}) \) \( 28q + 28q^{9} + 2q^{11} + 16q^{15} + 24q^{27} + 16q^{31} + 4q^{33} + 12q^{37} + 4q^{45} + 20q^{47} - 64q^{53} + 20q^{55} + 12q^{59} - 12q^{67} - 48q^{71} - 52q^{81} - 52q^{89} + 12q^{91} + 4q^{93} + 56q^{97} - 10q^{99} + O(q^{100}) \)

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.m.a \(28\) \(4.567\) None \(0\) \(0\) \(0\) \(0\)

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

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