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Properties

Label 18.16.c
Level $18$
Weight $16$
Character orbit 18.c
Rep. character $\chi_{18}(7,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $30$
Newform subspaces $2$
Sturm bound $48$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 16 \)
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: \(48\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(18, [\chi])\).

Total New Old
Modular forms 94 30 64
Cusp forms 86 30 56
Eisenstein series 8 0 8

Trace form

\( 30 q + 128 q^{2} - 4065 q^{3} - 245760 q^{4} + 149058 q^{5} - 1319040 q^{6} - 1607412 q^{7} - 4194304 q^{8} + 22300923 q^{9} + O(q^{10}) \) \( 30 q + 128 q^{2} - 4065 q^{3} - 245760 q^{4} + 149058 q^{5} - 1319040 q^{6} - 1607412 q^{7} - 4194304 q^{8} + 22300923 q^{9} - 10021173 q^{11} + 62619648 q^{12} + 83018184 q^{13} + 357435136 q^{14} + 670222170 q^{15} - 4026531840 q^{16} + 1893650970 q^{17} - 4388640000 q^{18} - 6129754950 q^{19} + 2442166272 q^{20} + 2737793988 q^{21} - 7841158272 q^{22} + 44800278504 q^{23} + 8524922880 q^{24} - 94064051319 q^{25} - 175840512512 q^{26} - 165500349552 q^{27} + 52671676416 q^{28} + 26026301244 q^{29} - 223191318528 q^{30} - 98844358566 q^{31} + 34359738368 q^{32} + 671507769033 q^{33} - 73029052800 q^{34} - 3831738869628 q^{35} + 133623791616 q^{36} - 1063196719680 q^{37} + 345485820544 q^{38} - 5130412492254 q^{39} + 4123029630573 q^{41} + 2199962689536 q^{42} - 1767331436979 q^{43} + 328373796864 q^{44} + 749545049898 q^{45} - 3195460154880 q^{46} + 2149488934548 q^{47} + 65229815808 q^{48} - 6652132211925 q^{49} + 4007268055424 q^{50} - 1708918576029 q^{51} + 1360169926656 q^{52} + 15784753623648 q^{53} + 8219398695552 q^{54} + 35370278956116 q^{55} + 5856217268224 q^{56} + 71516058958023 q^{57} - 9119633580288 q^{58} - 30350674138539 q^{59} - 9008138059776 q^{60} + 29855882058090 q^{61} + 44716607036416 q^{62} - 32066086933218 q^{63} + 131941395333120 q^{64} - 90147327219666 q^{65} + 90166908469248 q^{66} + 6388570299327 q^{67} - 15512788746240 q^{68} - 213939765240426 q^{69} + 81297526542336 q^{70} + 39714096273672 q^{71} - 52563913211904 q^{72} - 351226324561962 q^{73} + 4333484869120 q^{74} - 168864317783109 q^{75} + 50214952550400 q^{76} + 355411395607668 q^{77} + 20008680817920 q^{78} - 151141685596626 q^{79} - 80024904400896 q^{80} - 1152065996686377 q^{81} - 220317391266048 q^{82} + 189086594619750 q^{83} - 373308005646336 q^{84} - 166828885161012 q^{85} + 699880330583680 q^{86} + 38624745860388 q^{87} - 128469537128448 q^{88} - 2968936496396556 q^{89} - 969227346419712 q^{90} + 3063953296074540 q^{91} + 734007763009536 q^{92} + 1061678246398374 q^{93} - 502346270096640 q^{94} + 2589427476658584 q^{95} + 214404767416320 q^{96} + 2519620743113097 q^{97} - 2879592001375488 q^{98} - 4878086841309456 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{16}^{\mathrm{new}}(18, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
18.16.c.a 18.c 9.c $14$ $25.685$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-896\) \(0\) \(74529\) \(592525\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2^{7}-2^{7}\beta _{1})q^{2}+(-240-480\beta _{1}+\cdots)q^{3}+\cdots\)
18.16.c.b 18.c 9.c $16$ $25.685$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(1024\) \(-4065\) \(74529\) \(-2199937\) $\mathrm{SU}(2)[C_{3}]$ \(q+2^{7}\beta _{1}q^{2}+(-389+270\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{16}^{\mathrm{old}}(18, [\chi])\) into lower level spaces

\( S_{16}^{\mathrm{old}}(18, [\chi]) \cong \) \(S_{16}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)