Properties

Label 572.2.bb
Level $572$
Weight $2$
Character orbit 572.bb
Rep. character $\chi_{572}(51,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $320$
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.bb (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 572 \)
Character field: \(\Q(\zeta_{10})\)
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 352 352 0
Cusp forms 320 320 0
Eisenstein series 32 32 0

Trace form

\( 320q - 6q^{4} + 60q^{9} + O(q^{10}) \) \( 320q - 6q^{4} + 60q^{9} - 20q^{12} - 10q^{13} - 6q^{14} - 2q^{16} - 20q^{17} - 54q^{22} + 52q^{25} - 34q^{26} - 20q^{29} - 60q^{30} + 86q^{36} + 26q^{38} - 10q^{40} - 68q^{42} + 4q^{48} + 20q^{49} - 30q^{52} - 4q^{53} - 116q^{56} - 20q^{61} - 10q^{62} - 6q^{64} + 86q^{66} - 140q^{68} + 56q^{69} + 40q^{74} - 44q^{77} - 48q^{78} - 84q^{81} - 70q^{82} - 6q^{88} + 180q^{90} - 2q^{92} - 10q^{94} + O(q^{100}) \)

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.bb.a \(16\) \(4.567\) 16.0.\(\cdots\).9 \(\Q(\sqrt{-13}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{8}q^{2}+(2+2\beta _{2}-2\beta _{7}-2\beta _{9})q^{4}+\cdots\)
572.2.bb.b \(304\) \(4.567\) None \(0\) \(0\) \(0\) \(0\)