Space of modular forms of level 105, weight 10, and Character 105.b

• Label: 105.10.b
• Level: $105$
• Weight: $10$
• Character orbit: 105.b
• Rep. character: $\chi_{105}(41,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $2$
• Sturm bound: $160$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	105.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(160\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(105, [\chi])\).

	Total	New	Old
Modular forms	148	96	52
Cusp forms	140	96	44
Eisenstein series	8	0	8

Trace form

96 * q - 24576 * q^4 - 456 * q^7 - 32948 * q^9 + 132500 * q^15 + 5838576 * q^16 - 3060652 * q^18 + 873288 * q^21 + 1731096 * q^22 + 37500000 * q^25 + 2284260 * q^28 - 4760000 * q^30 - 24202824 * q^36 + 18157272 * q^37 - 2782116 * q^39 + 13077504 * q^42 - 144353928 * q^43 - 66762576 * q^46 + 84301152 * q^49 + 253354380 * q^51 - 264061152 * q^57 - 548081424 * q^58 + 241252500 * q^60 - 406939208 * q^63 - 602223360 * q^64 + 645790296 * q^67 + 588937500 * q^70 + 4005868552 * q^72 - 972004884 * q^78 - 762859752 * q^79 + 1342394140 * q^81 - 2205895464 * q^84 + 510030000 * q^85 - 1533173472 * q^88 + 4421339568 * q^91 + 2875414320 * q^93 - 5923419820 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(105, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
105.10.b.a	$105$	$10$	105.b	21.c	$2$	$48$	$48$	$54.079$		None		✓			105.10.b.a	$2$	$0$	\(0\)	\(-106\)	\(-30000\)	\(-228\)		$\mathrm{SU}(2)[C_{2}]$
105.10.b.b	$105$	$10$	105.b	21.c	$2$	$48$	$48$	$54.079$		None		✓			105.10.b.a	$2$	$0$	\(0\)	\(106\)	\(30000\)	\(-228\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{10}^{\mathrm{old}}(105, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(105, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)