Properties

Label 572.2.p
Level $572$
Weight $2$
Character orbit 572.p
Rep. character $\chi_{572}(309,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $24$
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.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
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 24 156
Cusp forms 156 24 132
Eisenstein series 24 0 24

Trace form

\( 24q - 2q^{3} + 6q^{7} - 14q^{9} + O(q^{10}) \) \( 24q - 2q^{3} + 6q^{7} - 14q^{9} - 2q^{13} - 6q^{19} + 10q^{23} - 40q^{25} - 8q^{27} - 8q^{29} + 8q^{35} + 18q^{37} + 36q^{41} + 10q^{43} - 30q^{45} + 14q^{49} + 44q^{51} + 16q^{53} - 24q^{59} + 6q^{61} - 6q^{63} - 24q^{65} - 54q^{67} + 10q^{69} + 18q^{71} + 6q^{75} - 16q^{77} - 32q^{79} - 4q^{81} + 52q^{87} - 18q^{89} - 18q^{91} + 30q^{93} - 12q^{95} + 42q^{97} + O(q^{100}) \)

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.p.a \(24\) \(4.567\) None \(0\) \(-2\) \(0\) \(6\)

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

\( S_{2}^{\mathrm{old}}(572, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(286, [\chi])\)\(^{\oplus 2}\)