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Properties

Label 18.8.c
Level $18$
Weight $8$
Character orbit 18.c
Rep. character $\chi_{18}(7,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $14$
Newform subspaces $2$
Sturm bound $24$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 18.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(18, [\chi])\).

Total New Old
Modular forms 46 14 32
Cusp forms 38 14 24
Eisenstein series 8 0 8

Trace form

\( 14 q + 8 q^{2} - 39 q^{3} - 448 q^{4} + 108 q^{5} + 1272 q^{6} + 166 q^{7} - 1024 q^{8} + 57 q^{9} + O(q^{10}) \) \( 14 q + 8 q^{2} - 39 q^{3} - 448 q^{4} + 108 q^{5} + 1272 q^{6} + 166 q^{7} - 1024 q^{8} + 57 q^{9} + 8751 q^{11} + 3694 q^{13} + 2032 q^{14} + 18360 q^{15} - 28672 q^{16} - 81762 q^{17} - 3408 q^{18} - 46778 q^{19} + 6912 q^{20} + 277854 q^{21} + 35256 q^{22} - 41682 q^{23} - 7680 q^{24} - 181369 q^{25} - 263840 q^{26} - 200880 q^{27} - 21248 q^{28} + 522930 q^{29} + 456192 q^{30} + 144892 q^{31} + 32768 q^{32} + 517473 q^{33} - 88728 q^{34} - 2580768 q^{35} - 335040 q^{36} - 278696 q^{37} + 912808 q^{38} + 2453976 q^{39} + 1697697 q^{41} - 403200 q^{42} - 384347 q^{43} - 1120128 q^{44} - 3451572 q^{45} + 602016 q^{46} + 987342 q^{47} + 159744 q^{48} - 790863 q^{49} + 1324184 q^{50} - 1970667 q^{51} + 236416 q^{52} + 66552 q^{53} - 581976 q^{54} + 1521936 q^{55} + 130048 q^{56} + 1182801 q^{57} - 346128 q^{58} + 2885649 q^{59} - 2059776 q^{60} + 4157908 q^{61} - 2344256 q^{62} - 4404036 q^{63} + 3670016 q^{64} - 2113236 q^{65} - 4022784 q^{66} - 6528545 q^{67} + 2616384 q^{68} + 9507348 q^{69} - 1620864 q^{70} + 11239752 q^{71} + 2320896 q^{72} + 13333186 q^{73} + 4648288 q^{74} - 22090299 q^{75} + 1496896 q^{76} - 12102258 q^{77} - 6015408 q^{78} - 10232468 q^{79} - 884736 q^{80} + 11656701 q^{81} - 7620624 q^{82} - 22434636 q^{83} - 8969856 q^{84} + 2938248 q^{85} - 1724696 q^{86} + 25741386 q^{87} + 2256384 q^{88} + 49866420 q^{89} + 46925568 q^{90} - 10938616 q^{91} - 2667648 q^{92} - 17811900 q^{93} - 5792592 q^{94} - 48359376 q^{95} - 4718592 q^{96} - 21483755 q^{97} - 28083408 q^{98} + 15105546 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(18, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
18.8.c.a 18.c 9.c $6$ $5.623$ 6.0.\(\cdots\).1 None \(-24\) \(-27\) \(54\) \(210\) $\mathrm{SU}(2)[C_{3}]$ \(q-8\beta _{1}q^{2}+(-14+19\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots\)
18.8.c.b 18.c 9.c $8$ $5.623$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(32\) \(-12\) \(54\) \(-44\) $\mathrm{SU}(2)[C_{3}]$ \(q+(8-8\beta _{1})q^{2}+(-7+11\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(18, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(18, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)