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

• Label: 105.2.j
• Level: $105$
• Weight: $2$
• Character orbit: 105.j
• Rep. character: $\chi_{105}(8,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $24$
• 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.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
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	40	24	16
Cusp forms	24	24	0
Eisenstein series	16	0	16

Trace form

24 * q - 4 * q^3 - 16 * q^10 + 16 * q^12 - 8 * q^13 - 16 * q^15 - 16 * q^16 - 20 * q^18 + 4 * q^21 + 8 * q^22 - 16 * q^25 - 16 * q^27 + 20 * q^30 + 28 * q^33 + 16 * q^36 - 16 * q^37 + 64 * q^40 - 20 * q^42 - 40 * q^43 + 20 * q^45 - 64 * q^46 + 16 * q^48 - 20 * q^51 + 40 * q^55 + 4 * q^57 + 40 * q^58 + 32 * q^60 + 32 * q^61 - 8 * q^63 - 16 * q^66 + 24 * q^67 - 8 * q^70 - 8 * q^72 + 32 * q^73 - 60 * q^75 + 32 * q^76 + 60 * q^78 + 52 * q^81 - 80 * q^82 + 24 * q^85 + 4 * q^87 + 96 * q^88 - 24 * q^90 - 24 * q^91 - 76 * q^93 - 96 * q^96 + 24 * 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.j.a	$105$	$2$	105.j	15.e	$4$	$24$	$12$	$0.838$		None		✓	✓	✓	105.2.j.a	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$