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Properties

Label 583.2.f
Level $583$
Weight $2$
Character orbit 583.f
Rep. character $\chi_{583}(76,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $104$
Newform subspaces $2$
Sturm bound $108$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 583 = 11 \cdot 53 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 583.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 583 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(108\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(583, [\chi])\).

Total New Old
Modular forms 112 112 0
Cusp forms 104 104 0
Eisenstein series 8 8 0

Trace form

\( 104 q - 2 q^{3} - 2 q^{5} + 8 q^{12} - 24 q^{14} + 4 q^{15} - 140 q^{16} + 12 q^{20} - 14 q^{22} - 2 q^{23} + 28 q^{26} - 2 q^{27} - 6 q^{31} + 24 q^{33} - 12 q^{34} + 68 q^{36} - 8 q^{42} + 20 q^{44} + 24 q^{45}+ \cdots + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(583, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
583.2.f.a 583.f 583.f $4$ $4.655$ \(\Q(i, \sqrt{11})\) \(\Q(\sqrt{-11}) \) 583.2.f.a \(0\) \(2\) \(6\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(\beta _{1}-\beta _{2})q^{3}+2\beta _{1}q^{4}+(2-\beta _{1}-\beta _{3})q^{5}+\cdots\)
583.2.f.b 583.f 583.f $100$ $4.655$ None 583.2.f.b \(0\) \(-4\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$