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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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(572, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
572.2.bb.a 572.bb 572.ab $16$ $4.567$ 16.0.\(\cdots\).9 \(\Q(\sqrt{-13}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{10}]$ \(q-\beta _{8}q^{2}+(2+2\beta _{2}-2\beta _{7}-2\beta _{9})q^{4}+\cdots\)
572.2.bb.b 572.bb 572.ab $304$ $4.567$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$