Properties

Label 572.2.n
Level $572$
Weight $2$
Character orbit 572.n
Rep. character $\chi_{572}(53,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $48$
Newform subspaces $2$
Sturm bound $168$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 572.n (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 2 \)
Sturm bound: \(168\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(572, [\chi])\).

Total New Old
Modular forms 360 48 312
Cusp forms 312 48 264
Eisenstein series 48 0 48

Trace form

\( 48q + 2q^{3} - 6q^{5} + 14q^{7} - 10q^{9} + O(q^{10}) \) \( 48q + 2q^{3} - 6q^{5} + 14q^{7} - 10q^{9} + 2q^{13} - 10q^{15} + 4q^{17} - 14q^{19} - 44q^{21} + 4q^{23} - 38q^{25} + 2q^{27} - 6q^{29} - 6q^{31} - 12q^{33} - 16q^{35} + 30q^{37} + 38q^{41} - 16q^{43} + 28q^{45} + 12q^{47} + 26q^{49} + 14q^{51} + 4q^{53} + 30q^{55} - 22q^{57} - 68q^{59} - 26q^{61} + 60q^{63} - 32q^{65} + 36q^{67} + 6q^{71} - 44q^{73} - 42q^{75} - 60q^{77} + 42q^{79} - 2q^{81} + 2q^{83} + 22q^{85} + 88q^{87} + 80q^{89} - 8q^{91} - 20q^{93} + 14q^{95} - 36q^{97} + 78q^{99} + O(q^{100}) \)

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.n.a \(20\) \(4.567\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(1\) \(1\) \(3\) \(q+\beta _{5}q^{3}+(-\beta _{9}-\beta _{10})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
572.2.n.b \(28\) \(4.567\) None \(0\) \(1\) \(-7\) \(11\)

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

\( S_{2}^{\mathrm{old}}(572, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(286, [\chi])\)\(^{\oplus 2}\)