Properties

Label 572.2.bq
Level $572$
Weight $2$
Character orbit 572.bq
Rep. character $\chi_{572}(49,\cdot)$
Character field $\Q(\zeta_{30})$
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.bq (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{30})\)
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

\( 112q + 20q^{9} + O(q^{10}) \) \( 112q + 20q^{9} - 6q^{11} + 11q^{13} + 30q^{15} + 16q^{17} - 12q^{19} + 6q^{23} + 40q^{25} - 12q^{27} - 5q^{29} + 9q^{33} - 33q^{35} - 45q^{39} - 18q^{41} + 30q^{45} - 16q^{49} + 48q^{51} - 2q^{53} - 20q^{55} - 39q^{59} + 4q^{61} - 102q^{63} - 6q^{65} + 48q^{67} + 34q^{69} + 84q^{71} - 56q^{75} - 22q^{77} - 24q^{79} + 16q^{81} + 60q^{85} - 34q^{87} - 66q^{89} - 41q^{91} + 123q^{93} + 12q^{95} - 15q^{97} + O(q^{100}) \)

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

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

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