Space of modular forms of level 5, weight 18, and Character 5.b

• Label: 5.18.b
• Level: $5$
• Weight: $18$
• Character orbit: 5.b
• Rep. character: $\chi_{5}(4,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $9$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	5.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(9\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(5, [\chi])\).

	Total	New	Old
Modular forms	10	10	0
Cusp forms	8	8	0
Eisenstein series	2	2	0

Trace form

8 * q - 579096 * q^4 + 379200 * q^5 + 357816 * q^6 - 234916344 * q^9 + 329570200 * q^10 + 463296576 * q^11 - 29937907992 * q^14 + 30646226400 * q^15 + 30848001568 * q^16 - 20615713280 * q^19 - 47558579400 * q^20 - 75039699024 * q^21 + 1768741136160 * q^24 - 1789249435000 * q^25 - 838901194224 * q^26 - 4079017824720 * q^29 + 2416984007400 * q^30 + 11329328658496 * q^31 - 36406243632832 * q^34 + 4019663899200 * q^35 + 59729752432728 * q^36 + 40318460422272 * q^39 - 209747532172000 * q^40 + 97217252847456 * q^41 - 116357853210912 * q^44 - 366841998003600 * q^45 + 1081224261700136 * q^46 - 856574357621656 * q^49 - 1283266301910000 * q^50 + 2468309514424896 * q^51 - 3408409774777680 * q^54 - 2042713226757600 * q^55 + 8363016326678880 * q^56 - 1091409512240640 * q^59 - 11479379108104800 * q^60 + 8064731010774976 * q^61 - 3616160324265856 * q^64 - 11989509557901600 * q^65 + 27318846906958752 * q^66 - 12078989597365008 * q^69 - 13190931213697800 * q^70 + 25241492058140736 * q^71 - 29902523510328912 * q^74 + 3839235716880000 * q^75 + 20767634734678560 * q^76 + 3229852337730880 * q^79 + 1263407265391200 * q^80 - 49353541005202632 * q^81 + 101439947332382688 * q^84 + 25693702369787200 * q^85 - 165112838769552744 * q^86 + 92963987535626640 * q^89 + 206315814421823400 * q^90 - 225591670236809664 * q^91 + 162612564681867848 * q^94 + 204319715505252000 * q^95 - 654303222993538944 * q^96 - 56327331239952768 * q^99

Decomposition of \(S_{18}^{\mathrm{new}}(5, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5.18.b.a	$5$	$18$	5.b	5.b	$2$	$8$	$8$	$9.161$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓	✓	✓	5.18.b.a	$2$	$0$	\(0\)	\(0\)	\(379200\)	\(0\)	$2^{21}\cdot 3^{8}\cdot 5^{12}\cdot 11$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-72387+\beta _{3}+\cdots)q^{4}+\cdots\)