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Properties

Label 9.7.d
Level $9$
Weight $7$
Character orbit 9.d
Rep. character $\chi_{9}(2,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $10$
Newform subspaces $1$
Sturm bound $7$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 9 = 3^{2} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 9.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(7\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(9, [\chi])\).

Total New Old
Modular forms 14 14 0
Cusp forms 10 10 0
Eisenstein series 4 4 0

Trace form

\( 10 q - 3 q^{2} + 24 q^{3} + 127 q^{4} - 219 q^{5} + 333 q^{6} - 121 q^{7} - 1980 q^{9} + O(q^{10}) \) \( 10 q - 3 q^{2} + 24 q^{3} + 127 q^{4} - 219 q^{5} + 333 q^{6} - 121 q^{7} - 1980 q^{9} - 132 q^{10} + 483 q^{11} - 1830 q^{12} - 841 q^{13} + 12174 q^{14} + 7965 q^{15} - 1985 q^{16} - 7884 q^{18} + 6176 q^{19} - 63186 q^{20} - 25845 q^{21} + 3471 q^{22} + 53565 q^{23} + 111519 q^{24} + 8452 q^{25} - 101034 q^{27} - 22660 q^{28} - 80679 q^{29} - 37782 q^{30} - 24601 q^{31} + 218295 q^{32} + 229995 q^{33} + 7425 q^{34} - 274977 q^{36} + 12764 q^{37} - 371877 q^{38} - 112749 q^{39} + 54150 q^{40} + 232251 q^{41} + 270540 q^{42} - 93271 q^{43} + 63801 q^{45} + 112512 q^{46} - 142887 q^{47} - 143283 q^{48} + 86238 q^{49} + 318459 q^{50} + 57078 q^{51} + 186920 q^{52} + 13851 q^{54} - 419982 q^{55} + 342546 q^{56} - 1086 q^{57} - 380658 q^{58} - 995061 q^{59} - 1011402 q^{60} - 59305 q^{61} + 526455 q^{63} + 403066 q^{64} + 1642029 q^{65} + 1610586 q^{66} + 158513 q^{67} - 1693791 q^{68} - 851715 q^{69} - 304788 q^{70} + 1469907 q^{72} + 933896 q^{73} + 595182 q^{74} - 757524 q^{75} + 666641 q^{76} - 2198883 q^{77} - 3481884 q^{78} + 468707 q^{79} + 1774548 q^{81} - 2038470 q^{82} + 3008337 q^{83} + 1543746 q^{84} - 1189944 q^{85} + 1905549 q^{86} - 615591 q^{87} - 349773 q^{88} + 84294 q^{90} - 211778 q^{91} - 973788 q^{92} - 2954553 q^{93} + 809124 q^{94} - 2562954 q^{95} - 1022112 q^{96} + 336029 q^{97} - 432567 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(9, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
9.7.d.a 9.d 9.d $10$ $2.070$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-3\) \(24\) \(-219\) \(-121\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{1}q^{2}+(2+\beta _{1}-\beta _{2}+\beta _{3}+\beta _{6}+\cdots)q^{3}+\cdots\)