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

• Label: 105.2.d
• Level: $105$
• Weight: $2$
• Character orbit: 105.d
• Rep. character: $\chi_{105}(64,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $32$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(32\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	20	8	12
Cusp forms	12	8	4
Eisenstein series	8	0	8

Trace form

\( 8 q - 8 q^{4} + 4 q^{5} - 4 q^{6} - 8 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
105.2.d.a	$105$	$2$	105.d	5.b	$2$	$2$	$2$	$0.838$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}+q^{4}+(1-2i)q^{5}-q^{6}+\cdots\)
105.2.d.b	$105$	$2$	105.d	5.b	$2$	$6$	$6$	$0.838$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{3}+\beta _{5})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(105, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(105, [\chi]) \cong \)