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Properties

Label 473.2.k
Level $473$
Weight $2$
Character orbit 473.k
Rep. character $\chi_{473}(85,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $168$
Newform subspaces $2$
Sturm bound $88$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 473 = 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 473.k (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 473 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(88\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(473, [\chi])\).

Total New Old
Modular forms 184 184 0
Cusp forms 168 168 0
Eisenstein series 16 16 0

Trace form

\( 168 q - 42 q^{4} - 20 q^{6} + 44 q^{9} + O(q^{10}) \) \( 168 q - 42 q^{4} - 20 q^{6} + 44 q^{9} - 4 q^{11} - 15 q^{13} - 12 q^{14} - 10 q^{15} - 10 q^{16} - 54 q^{23} + 40 q^{24} + 44 q^{25} - 8 q^{31} - 100 q^{35} + 6 q^{36} - 70 q^{38} - 40 q^{40} - 10 q^{41} - 24 q^{44} + 30 q^{47} - 74 q^{49} - 130 q^{52} - 30 q^{53} + 132 q^{56} + 20 q^{57} + 4 q^{58} + 22 q^{59} + 66 q^{60} + 46 q^{64} + 80 q^{66} - 18 q^{67} - 160 q^{68} + 100 q^{74} - 64 q^{78} - 70 q^{79} + 22 q^{81} - 20 q^{83} + 220 q^{84} + 16 q^{86} + 260 q^{90} + 46 q^{92} + 20 q^{95} + 70 q^{96} - 75 q^{97} - 155 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(473, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
473.2.k.a 473.k 473.k $8$ $3.777$ 8.0.\(\cdots\).1 \(\Q(\sqrt{-43}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{10}]$ \(q-2\beta _{2}q^{4}+(-3-3\beta _{2}+3\beta _{4}-3\beta _{6}+\cdots)q^{9}+\cdots\)
473.2.k.b 473.k 473.k $160$ $3.777$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$