Properties

Label 36.9.f
Level $36$
Weight $9$
Character orbit 36.f
Rep. character $\chi_{36}(7,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $92$
Newform subspaces $1$
Sturm bound $54$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 36.f (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(54\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(36, [\chi])\).

Total New Old
Modular forms 100 100 0
Cusp forms 92 92 0
Eisenstein series 8 8 0

Trace form

\( 92 q - q^{2} - q^{4} - 2 q^{5} + 1359 q^{6} - 9958 q^{8} - 1908 q^{9} + O(q^{10}) \) \( 92 q - q^{2} - q^{4} - 2 q^{5} + 1359 q^{6} - 9958 q^{8} - 1908 q^{9} + 508 q^{10} - 25668 q^{12} - 2 q^{13} - 9348 q^{14} - q^{16} + 27544 q^{17} - 558168 q^{18} + 26260 q^{20} + 157722 q^{21} - 513 q^{22} + 36633 q^{24} - 2968752 q^{25} - 2625752 q^{26} - 131076 q^{28} - 632546 q^{29} + 3910260 q^{30} - 4303321 q^{32} + 3423594 q^{33} + 874897 q^{34} + 2094867 q^{36} - 8 q^{37} + 5021955 q^{38} - 101876 q^{40} + 3438958 q^{41} - 1253550 q^{42} + 4513722 q^{44} + 4527390 q^{45} - 8607912 q^{46} - 6410637 q^{48} + 28000460 q^{49} - 4611225 q^{50} + 4952398 q^{52} + 7237432 q^{53} + 1445961 q^{54} + 16638318 q^{56} + 27312 q^{57} - 6359024 q^{58} - 19327032 q^{60} - 2 q^{61} + 64961196 q^{62} - 11896126 q^{64} - 179134 q^{65} - 62514462 q^{66} + 37085155 q^{68} - 93014982 q^{69} + 6546306 q^{70} - 94972077 q^{72} - 32396456 q^{73} - 19652372 q^{74} - 14869203 q^{76} - 11357382 q^{77} - 58314714 q^{78} + 26901520 q^{80} - 109921044 q^{81} + 98754394 q^{82} + 48970518 q^{84} - 781252 q^{85} + 60280257 q^{86} - 15010485 q^{88} + 32208376 q^{89} - 119152692 q^{90} - 66511734 q^{92} + 127902330 q^{93} + 125494500 q^{94} - 151076052 q^{96} - 56298482 q^{97} - 17303818 q^{98} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(36, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
36.9.f.a 36.f 36.f $92$ $14.666$ None 36.9.f.a \(-1\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$