Properties

Label 572.2.x
Level $572$
Weight $2$
Character orbit 572.x
Rep. character $\chi_{572}(25,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $56$
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.x (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{10})\)
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 360 56 304
Cusp forms 312 56 256
Eisenstein series 48 0 48

Trace form

\( 56q - 2q^{9} + O(q^{10}) \) \( 56q - 2q^{9} + q^{13} - 10q^{17} + 12q^{23} + 2q^{25} + 12q^{27} + 44q^{29} - 42q^{35} + 15q^{39} + 48q^{43} - 2q^{49} - 12q^{51} - 22q^{53} - 40q^{55} - 4q^{61} - 6q^{65} + 8q^{69} + 20q^{75} - 2q^{77} + 48q^{79} - 130q^{81} - 20q^{87} + 47q^{91} + 12q^{95} + O(q^{100}) \)

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.x.a \(56\) \(4.567\) None \(0\) \(0\) \(0\) \(0\)

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

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