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

• Label: 105.4.g
• Level: $105$
• Weight: $4$
• Character orbit: 105.g
• Rep. character: $\chi_{105}(104,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $2$
• Sturm bound: $64$
• Trace bound: $1$

Defining parameters

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

Dimensions

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

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

Trace form

44 * q + 152 * q^4 - 48 * q^9 + 12 * q^15 + 440 * q^16 - 48 * q^21 + 212 * q^25 - 336 * q^30 - 1104 * q^36 - 252 * q^39 - 1488 * q^46 - 124 * q^49 + 1620 * q^51 + 384 * q^60 - 2008 * q^64 - 3000 * q^70 - 248 * q^79 + 3072 * q^81 - 624 * q^84 + 208 * q^85 + 1864 * q^91 + 6396 * 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.g.a	$105$	$4$	105.g	105.g	$2$	$4$	$4$	$6.195$	\(\Q(\sqrt{-5}, \sqrt{7})\)	\(\Q(\sqrt{-35}) \)		✓			105.4.g.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+(2\beta _{1}-\beta _{3})q^{3}-8q^{4}-5\beta _{1}q^{5}+7\beta _{3}q^{7}+\cdots\)
105.4.g.b	$105$	$4$	105.g	105.g	$2$	$40$	$40$	$6.195$		None		✓	✓		105.4.g.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$