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Properties

Label 9.9.d
Level $9$
Weight $9$
Character orbit 9.d
Rep. character $\chi_{9}(2,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $14$
Newform subspaces $1$
Sturm bound $9$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 9 = 3^{2} \)
Weight: \( k \) \(=\) \( 9 \)
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: \(9\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 18 18 0
Cusp forms 14 14 0
Eisenstein series 4 4 0

Trace form

\( 14 q - 3 q^{2} - 93 q^{3} + 767 q^{4} + 438 q^{5} - 2259 q^{6} + 922 q^{7} + 17973 q^{9} + O(q^{10}) \) \( 14 q - 3 q^{2} - 93 q^{3} + 767 q^{4} + 438 q^{5} - 2259 q^{6} + 922 q^{7} + 17973 q^{9} - 516 q^{10} - 28677 q^{11} - 55110 q^{12} + 1684 q^{13} + 120966 q^{14} - 75276 q^{15} - 65281 q^{16} + 243324 q^{18} - 269630 q^{19} + 539454 q^{20} + 354054 q^{21} + 61311 q^{22} - 1000452 q^{23} - 1125513 q^{24} + 65177 q^{25} - 524826 q^{27} + 1075708 q^{28} + 3797682 q^{29} + 2372562 q^{30} - 164132 q^{31} - 8461881 q^{32} - 5761521 q^{33} + 654993 q^{34} + 12958047 q^{36} - 1671668 q^{37} + 10967691 q^{38} + 3383976 q^{39} + 613326 q^{40} - 10239447 q^{41} - 35844228 q^{42} + 791815 q^{43} + 27631638 q^{45} + 1189536 q^{46} + 31148628 q^{47} + 17088189 q^{48} - 4826637 q^{49} - 63849453 q^{50} - 47946573 q^{51} - 5552720 q^{52} + 36967995 q^{54} + 8107476 q^{55} + 116638674 q^{56} + 37276797 q^{57} + 14211822 q^{58} - 83493795 q^{59} - 109012050 q^{60} - 5255600 q^{61} + 38322432 q^{63} - 26813830 q^{64} + 69232992 q^{65} + 36133866 q^{66} - 8288855 q^{67} - 77746743 q^{68} - 62108640 q^{69} + 27813756 q^{70} + 88821171 q^{72} - 36721682 q^{73} - 10383450 q^{74} + 13792011 q^{75} - 42822959 q^{76} + 56158710 q^{77} + 27355140 q^{78} - 32771822 q^{79} - 16336971 q^{81} + 236099418 q^{82} - 198915996 q^{83} - 187060614 q^{84} + 97486146 q^{85} + 146190669 q^{86} + 114294006 q^{87} + 24955827 q^{88} - 222035850 q^{90} - 201514504 q^{91} - 295365804 q^{92} + 94187784 q^{93} - 36698244 q^{94} + 386813838 q^{95} + 768275928 q^{96} + 127049161 q^{97} - 511060752 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
9.9.d.a 9.d 9.d $14$ $3.666$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-3\) \(-93\) \(438\) \(922\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{1}q^{2}+(-5-3\beta _{3}+\beta _{4}+\beta _{6})q^{3}+\cdots\)