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

• Label: 15.18.b
• Level: $15$
• Weight: $18$
• Character orbit: 15.b
• Rep. character: $\chi_{15}(4,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	15.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(36\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	36	16	20
Cusp forms	32	16	16
Eisenstein series	4	0	4

Trace form

16 * q - 862698 * q^4 + 292740 * q^5 - 2480058 * q^6 - 688747536 * q^9 - 158256910 * q^10 + 907386144 * q^11 + 38248328748 * q^14 - 11415352680 * q^15 + 64410639650 * q^16 + 44375877728 * q^19 + 124652464020 * q^20 - 20437095096 * q^21 + 219244567374 * q^24 + 1631404456600 * q^25 + 2940223801452 * q^26 - 5348468604504 * q^29 - 6441904596780 * q^30 - 16935964052224 * q^31 + 60848757680284 * q^34 + 25456583995440 * q^35 + 37136320113258 * q^36 + 44207617726512 * q^39 + 246023763543250 * q^40 - 4873344779184 * q^41 + 224598182313996 * q^44 - 12601497105540 * q^45 - 1042392874396424 * q^46 + 85575569613760 * q^49 + 669894278364600 * q^50 - 640351191010752 * q^51 + 106758364789818 * q^54 + 2661435553553280 * q^55 - 8893968141042660 * q^56 + 2882362957102272 * q^59 + 3680941291545510 * q^60 - 6340947108203680 * q^61 + 2538830661242878 * q^64 + 13690132732535880 * q^65 - 10330303385194884 * q^66 + 6599935349396928 * q^69 + 10824491372201640 * q^70 - 11739285749899008 * q^71 - 6749027807219172 * q^74 - 2439088433863200 * q^75 - 32687788759104192 * q^76 + 28655274740363840 * q^79 - 7449390713147460 * q^80 + 29648323021629456 * q^81 - 35925592092243948 * q^84 + 27636069676463240 * q^85 + 261659254088221464 * q^86 - 119080233211377312 * q^89 + 6812441051092110 * q^90 + 201912942604136256 * q^91 - 186654825194113808 * q^94 - 434666709576297600 * q^95 - 40354765976105406 * q^96 - 39059998180033824 * q^99

Decomposition of \(S_{18}^{\mathrm{new}}(15, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
15.18.b.a	$15$	$18$	15.b	5.b	$2$	$16$	$16$	$27.483$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓	✓	15.18.b.a	$2$	$0$	\(0\)	\(0\)	\(292740\)	\(0\)	$2^{30}\cdot 3^{60}\cdot 5^{23}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+(-53919+\cdots)q^{4}+\cdots\)

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

\( S_{18}^{\mathrm{old}}(15, [\chi]) \simeq \) \(S_{18}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)