Space of modular forms of level 105, weight 4, and Character 105.p

• Label: 105.4.p
• Level: $105$
• Weight: $4$
• Character orbit: 105.p
• Rep. character: $\chi_{105}(59,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $88$
• Newform subspaces: $1$
• Sturm bound: $64$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.p (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(64\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(105, [\chi])\).

	Total	New	Old
Modular forms	104	104	0
Cusp forms	88	88	0
Eisenstein series	16	16	0

Trace form

88 * q - 164 * q^4 + 30 * q^10 + 114 * q^15 - 548 * q^16 - 228 * q^19 + 300 * q^21 + 72 * q^24 + 160 * q^25 - 318 * q^30 + 816 * q^31 - 336 * q^36 - 336 * q^39 + 30 * q^40 + 1377 * q^45 - 1296 * q^46 + 688 * q^49 + 138 * q^51 + 2268 * q^54 - 1866 * q^60 + 1392 * q^61 + 2248 * q^64 - 2772 * q^66 + 150 * q^70 - 765 * q^75 - 1528 * q^79 + 2844 * q^81 - 5160 * q^84 - 1084 * q^85 - 5632 * q^91 + 4416 * q^94 - 3456 * q^96 - 660 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(105, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
105.4.p.a	$105$	$4$	105.p	105.p	$6$	$88$	$44$	$6.195$		None		✓	✓	✓	105.4.p.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$