Space of modular forms of level 105, weight 2, and Character 105.x

• Label: 105.2.x
• Level: $105$
• Weight: $2$
• Character orbit: 105.x
• Rep. character: $\chi_{105}(2,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $32$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.x (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(32\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(105, [\chi])\).

	Total	New	Old
Modular forms	80	80	0
Cusp forms	48	48	0
Eisenstein series	32	32	0

Trace form

48 * q - 2 * q^3 - 24 * q^6 - 12 * q^7 - 8 * q^10 - 10 * q^12 - 16 * q^13 + 4 * q^15 - 8 * q^16 + 14 * q^18 - 28 * q^21 - 8 * q^22 + 4 * q^25 + 40 * q^27 - 60 * q^28 + 40 * q^30 - 24 * q^31 - 4 * q^33 + 8 * q^36 + 4 * q^37 - 16 * q^40 + 14 * q^42 + 16 * q^43 + 40 * q^45 - 32 * q^46 + 44 * q^48 + 8 * q^51 + 36 * q^52 - 40 * q^55 - 88 * q^57 + 56 * q^58 - 50 * q^60 - 8 * q^61 + 44 * q^63 + 76 * q^66 + 12 * q^67 + 140 * q^70 - 34 * q^72 + 52 * q^73 + 6 * q^75 + 64 * q^76 - 120 * q^78 + 20 * q^81 + 104 * q^82 - 24 * q^85 - 46 * q^87 - 84 * q^90 + 72 * q^91 - 44 * q^93 + 12 * q^96 - 120 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(105, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
105.2.x.a	$105$	$2$	105.x	105.x	$12$	$48$	$12$	$0.838$		None		✓	✓	✓	105.2.x.a	$8$	$0$	\(0\)	\(-2\)	\(0\)	\(-12\)		$\mathrm{SU}(2)[C_{12}]$