Space of modular forms of level 10, weight 18, and Character 10.b

• Label: 10.18.b
• Level: $10$
• Weight: $18$
• Character orbit: 10.b
• Rep. character: $\chi_{10}(9,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $27$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	10.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(27\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(10, [\chi])\).

	Total	New	Old
Modular forms	28	8	20
Cusp forms	24	8	16
Eisenstein series	4	0	4

Trace form

8 * q - 524288 * q^4 - 1225560 * q^5 - 974848 * q^6 - 363182504 * q^9 - 140779520 * q^10 + 146232096 * q^11 + 14260494336 * q^14 - 39815002720 * q^15 + 34359738368 * q^16 - 54264178080 * q^19 + 80318300160 * q^20 + 515442333056 * q^21 + 63887638528 * q^24 + 1013225778600 * q^25 - 2693383569408 * q^26 + 1660243083120 * q^29 + 4536489205760 * q^30 - 6055476993664 * q^31 + 14158246445056 * q^34 - 8725233780960 * q^35 + 23801528582144 * q^36 - 60047234232768 * q^39 + 9226126622720 * q^40 - 219921829971984 * q^41 - 9583466643456 * q^44 + 503517880841080 * q^45 - 136753191067648 * q^46 + 797208944041464 * q^49 + 535409908531200 * q^50 - 2629370351530624 * q^51 + 1870704820633600 * q^54 + 1370380127176480 * q^55 - 934575756804096 * q^56 - 155410557761760 * q^59 + 2609316018257920 * q^60 - 6350444068968944 * q^61 - 2251799813685248 * q^64 + 10508144084782080 * q^65 - 10180424127512576 * q^66 + 20821360231259392 * q^69 - 1051117677240320 * q^70 - 33149026543733184 * q^71 + 6017648345726976 * q^74 + 17427320439323200 * q^75 + 3556257174650880 * q^76 - 19354668791708160 * q^79 - 5263740119285760 * q^80 + 54432374624835848 * q^81 - 33780028739158016 * q^84 - 71530234876895360 * q^85 + 29616028444434432 * q^86 - 43569230299558320 * q^89 - 33153706682736640 * q^90 + 333420307889971776 * q^91 - 11440296922292224 * q^94 - 131478039235197600 * q^95 - 4186940278571008 * q^96 - 236681336419250848 * q^99

Decomposition of \(S_{18}^{\mathrm{new}}(10, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
10.18.b.a	$10$	$18$	10.b	5.b	$2$	$8$	$8$	$18.322$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓	✓	✓	10.18.b.a	$2$	$0$	\(0\)	\(0\)	\(-1225560\)	\(0\)	$2^{40}\cdot 3^{4}\cdot 5^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(-2\beta _{1}-\beta _{2})q^{3}-2^{16}q^{4}+\cdots\)

Decomposition of \(S_{18}^{\mathrm{old}}(10, [\chi])\) into lower level spaces

\( S_{18}^{\mathrm{old}}(10, [\chi]) \simeq \) \(S_{18}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)