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Properties

Label 473.2.d
Level $473$
Weight $2$
Character orbit 473.d
Rep. character $\chi_{473}(472,\cdot)$
Character field $\Q$
Dimension $42$
Newform subspaces $5$
Sturm bound $88$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 473 = 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 473.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 473 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(88\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

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

Total New Old
Modular forms 46 46 0
Cusp forms 42 42 0
Eisenstein series 4 4 0

Trace form

\( 42 q + 32 q^{4} - 54 q^{9} + O(q^{10}) \) \( 42 q + 32 q^{4} - 54 q^{9} - q^{11} - 8 q^{14} + 20 q^{16} + 14 q^{23} - 34 q^{25} + 18 q^{31} - 56 q^{36} + 14 q^{44} - 20 q^{47} + 14 q^{49} + 10 q^{53} - 112 q^{56} - 4 q^{58} + 8 q^{59} + 24 q^{60} - 36 q^{64} + 80 q^{66} - 2 q^{67} - 36 q^{78} + 58 q^{81} - 56 q^{86} + 24 q^{92} + 10 q^{97} - 35 q^{99} + O(q^{100}) \)

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.d.a 473.d 473.d $2$ $3.777$ \(\Q(\sqrt{-43}) \) \(\Q(\sqrt{-43}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{4}+3q^{9}+(1-\beta )q^{11}+(-1+2\beta )q^{13}+\cdots\)
473.2.d.b 473.d 473.d $4$ $3.777$ \(\Q(\sqrt{-2}, \sqrt{13})\) None \(-2\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(1+\beta _{3})q^{4}+\cdots\)
473.2.d.c 473.d 473.d $4$ $3.777$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}-2q^{4}+\beta _{3}q^{5}+(-2\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
473.2.d.d 473.d 473.d $4$ $3.777$ \(\Q(\sqrt{-2}, \sqrt{13})\) None \(2\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(1+\beta _{3})q^{4}+\cdots\)
473.2.d.e 473.d 473.d $28$ $3.777$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$