Space of modular forms of level 18, weight 15, and Character 18.b

• Label: 18.15.b
• Level: $18$
• Weight: $15$
• Character orbit: 18.b
• Rep. character: $\chi_{18}(17,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $45$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$18 = 2 \cdot 3^{2}$
Weight:	$k$	$=$	$15$
Character orbit:	$[\chi]$	$=$	18.b (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$3$
Character field:			$\Q$
Newform subspaces:			$2$
Sturm bound:			$45$
Trace bound:			$1$
Distinguishing $T_p$:			$5$

Dimensions

The following table gives the dimensions of various subspaces of $M_{15}(18, [\chi])$.

	Total	New	Old
Modular forms	46	6	40
Cusp forms	38	6	32
Eisenstein series	8	0	8

Trace form

6 * q - 49152 * q^4 + 2137512 * q^7 + 3900672 * q^10 + 193537776 * q^13 + 402653184 * q^16 + 970963104 * q^19 - 4600747008 * q^22 - 39166275126 * q^25 - 17510498304 * q^28 - 27571769016 * q^31 - 90482026752 * q^34 + 156645998292 * q^37 - 31954305024 * q^40 + 493032786960 * q^43 - 1446512495616 * q^46 + 1604536361082 * q^49 - 1585461460992 * q^52 + 8349283516464 * q^55 - 6511660307712 * q^58 + 17518543587660 * q^61 - 3298534883328 * q^64 - 3157091465424 * q^67 - 47802129159168 * q^70 - 17587701663072 * q^73 - 7954129747968 * q^76 - 17896719632136 * q^79 + 20727242166528 * q^82 + 14080782595932 * q^85 + 37689319489536 * q^88 + 204879580726848 * q^91 + 179372957598720 * q^94 - 210050877918048 * q^97

Decomposition of $S_{15}^{\mathrm{new}}(18, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
18.15.b.a	$18$	$15$	18.b	3.b	$2$	$2$	$2$	$22.379$	$\Q(\sqrt{-2})$	None		✓			18.15.b.a	$2$	$0$	$0$	$0$	$0$	$-522152$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-2^{6}\beta q^{2}-2^{13}q^{4}+9075\beta q^{5}-261076q^{7}+\cdots$
18.15.b.b	$18$	$15$	18.b	3.b	$2$	$4$	$4$	$22.379$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None		✓	✓		18.15.b.b	$2$	$0$	$0$	$0$	$0$	$2659664$	$2^{7}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+2^{6}\beta _{1}q^{2}-2^{13}q^{4}+(-3081\beta _{1}+\cdots)q^{5}+\cdots$

Decomposition of $S_{15}^{\mathrm{old}}(18, [\chi])$ into lower level spaces

$S_{15}^{\mathrm{old}}(18, [\chi]) \simeq$ $S_{15}^{\mathrm{new}}(3, [\chi])$$^{\oplus 4}$$\oplus$$S_{15}^{\mathrm{new}}(6, [\chi])$$^{\oplus 2}$$\oplus$$S_{15}^{\mathrm{new}}(9, [\chi])$$^{\oplus 2}$