Space of modular forms of level 18, weight 9, and Character 18.d

• Label: 18.9.d
• Level: $18$
• Weight: $9$
• Character orbit: 18.d
• Rep. character: $\chi_{18}(5,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $27$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	18.d (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(27\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(18, [\chi])\).

	Total	New	Old
Modular forms	52	16	36
Cusp forms	44	16	28
Eisenstein series	8	0	8

Trace form

16 * q + 126 * q^3 + 1024 * q^4 - 882 * q^5 + 384 * q^6 - 1846 * q^7 - 28662 * q^9 + 45756 * q^11 + 5376 * q^12 - 3370 * q^13 - 94464 * q^14 + 128754 * q^15 - 131072 * q^16 - 236544 * q^18 + 362180 * q^19 - 112896 * q^20 - 299166 * q^21 - 61824 * q^22 + 1311138 * q^23 - 147456 * q^24 + 963394 * q^25 - 208656 * q^27 - 472576 * q^28 - 2851290 * q^29 - 1253376 * q^30 + 542438 * q^31 + 3875796 * q^33 + 220416 * q^34 - 3655680 * q^36 + 3343328 * q^37 - 1314432 * q^38 - 5896002 * q^39 + 9218592 * q^41 + 14237952 * q^42 + 339512 * q^43 - 32740578 * q^45 + 7417344 * q^46 - 34980606 * q^47 - 1376256 * q^48 - 2364654 * q^49 + 27744768 * q^50 + 50877810 * q^51 + 431360 * q^52 - 5648256 * q^54 - 4584276 * q^55 - 12091392 * q^56 - 34049898 * q^57 - 7852800 * q^58 + 93924216 * q^59 + 18604800 * q^60 - 841954 * q^61 - 14043234 * q^63 - 33554432 * q^64 - 126568134 * q^65 - 35179776 * q^66 + 29946644 * q^67 - 5476608 * q^68 + 70499610 * q^69 - 34359552 * q^70 - 11894784 * q^72 - 7547764 * q^73 + 35124480 * q^74 + 114494910 * q^75 + 23179520 * q^76 + 9309294 * q^77 + 23014656 * q^78 + 33813002 * q^79 - 46018134 * q^81 - 137346048 * q^82 + 114200226 * q^83 - 15040512 * q^84 - 125696772 * q^85 - 171379584 * q^86 - 159599970 * q^87 + 7913472 * q^88 + 129745152 * q^90 + 268578316 * q^91 + 167825664 * q^92 + 120711534 * q^93 - 11832576 * q^94 - 143949240 * q^95 - 25165824 * q^96 - 89415484 * q^97 + 366888330 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(18, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
18.9.d.a	$18$	$9$	18.d	9.d	$6$	$16$	$8$	$7.333$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓	✓	18.9.d.a	$2$	$0$	\(0\)	\(126\)	\(-882\)	\(-1846\)	$2^{28}\cdot 3^{22}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{4}q^{2}+(7+2\beta _{1}+\beta _{3}+\beta _{4})q^{3}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(18, [\chi])\) into lower level spaces

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