Properties

Label 731.2.d
Level $731$
Weight $2$
Character orbit 731.d
Rep. character $\chi_{731}(560,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $4$
Sturm bound $132$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 731 = 17 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 731.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(132\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(731, [\chi])\).

Total New Old
Modular forms 68 64 4
Cusp forms 64 64 0
Eisenstein series 4 0 4

Trace form

\( 64 q - 2 q^{2} + 58 q^{4} - 6 q^{8} - 76 q^{9} + O(q^{10}) \) \( 64 q - 2 q^{2} + 58 q^{4} - 6 q^{8} - 76 q^{9} - 10 q^{13} + 12 q^{15} + 62 q^{16} + 7 q^{17} - 2 q^{18} + 20 q^{19} + 8 q^{21} - 60 q^{25} - 16 q^{26} + 16 q^{30} + 6 q^{32} + 20 q^{33} - 36 q^{34} + 4 q^{35} - 78 q^{36} + 4 q^{38} + 12 q^{42} - 4 q^{43} - 12 q^{47} - 52 q^{49} - 10 q^{50} + 26 q^{51} - 52 q^{52} - 6 q^{53} - 24 q^{59} + 12 q^{60} + 30 q^{64} - 20 q^{66} - 22 q^{67} + 52 q^{68} - 12 q^{69} + 100 q^{70} - 46 q^{72} + 16 q^{76} + 4 q^{77} + 104 q^{81} - 18 q^{83} + 28 q^{84} + 12 q^{85} + 10 q^{86} + 40 q^{87} - 36 q^{89} + 24 q^{93} - 96 q^{94} + 30 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(731, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
731.2.d.a 731.d 17.b $2$ $5.837$ \(\Q(\sqrt{-2}) \) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-q^{4}+\beta q^{5}-3q^{8}+3q^{9}+\beta q^{10}+\cdots\)
731.2.d.b 731.d 17.b $8$ $5.837$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-2q^{4}-\beta _{3}q^{5}+(\beta _{1}-\beta _{7})q^{7}+\cdots\)
731.2.d.c 731.d 17.b $20$ $5.837$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{2}+\beta _{13}q^{3}+(2+\beta _{1})q^{4}+\beta _{10}q^{5}+\cdots\)
731.2.d.d 731.d 17.b $34$ $5.837$ None \(-6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$