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

• Label: 105.4.d
• Level: $105$
• Weight: $4$
• Character orbit: 105.d
• Rep. character: $\chi_{105}(64,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• 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.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
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	16	36
Cusp forms	44	16	28
Eisenstein series	8	0	8

Trace form

\( 16 q - 60 q^{4} - 28 q^{5} - 12 q^{6} - 144 q^{9} + O(q^{10}) \)

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.d.a	$105$	$4$	105.d	5.b	$2$	$6$	$6$	$6.195$	6.0.84052224.1	None		✓			105.4.d.a	$2$	$0$	\(0\)	\(0\)	\(-14\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-3\beta _{3}q^{3}+(-1-2\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
105.4.d.b	$105$	$4$	105.d	5.b	$2$	$10$	$10$	$6.195$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓	✓		105.4.d.b	$2$	$0$	\(0\)	\(0\)	\(-14\)	\(0\)	$2^{9}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}-3\beta _{2}q^{3}+(-5-\beta _{1}+\beta _{5}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(105, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(105, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)