Properties

Label 572.2.bc
Level $572$
Weight $2$
Character orbit 572.bc
Rep. character $\chi_{572}(197,\cdot)$
Character field $\Q(\zeta_{12})$
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.bc (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{12})\)
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

\( 56q - 28q^{9} + O(q^{10}) \) \( 56q - 28q^{9} + 4q^{11} + 8q^{15} - 12q^{23} - 24q^{27} - 4q^{31} - 10q^{33} - 12q^{37} - 64q^{45} - 8q^{47} + 40q^{53} + 22q^{55} + 48q^{59} - 36q^{67} - 48q^{71} + 120q^{75} + 28q^{81} + 28q^{89} + 36q^{91} + 20q^{93} - 68q^{97} - 44q^{99} + O(q^{100}) \)

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

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

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