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 - 8 * q^10 + 4 * q^15 + 24 * q^16 - 28 * q^20 + 4 * q^21 + 12 * q^24 - 8 * q^25 + 24 * q^26 - 12 * q^30 - 16 * q^31 + 32 * q^34 + 4 * q^35 + 8 * q^36 - 8 * q^39 + 16 * q^40 + 8 * q^41 - 32 * q^44 - 4 * q^45 - 16 * q^46 - 8 * q^49 - 8 * q^50 + 8 * q^51 + 4 * q^54 - 8 * q^55 - 24 * q^56 - 16 * q^59 - 4 * q^60 - 16 * q^61 - 40 * q^64 + 24 * q^65 + 8 * q^66 + 8 * q^69 + 8 * q^70 + 32 * q^71 + 80 * q^74 + 16 * q^75 + 16 * q^76 - 32 * q^79 + 44 * q^80 + 8 * q^81 - 12 * q^84 + 16 * q^85 - 40 * q^89 + 8 * q^90 + 16 * q^91 + 32 * q^94 + 16 * q^95 - 68 * q^96

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.d.a	$105$	$2$	105.d	5.b	$2$	$2$	$2$	$0.838$	\(\Q(\sqrt{-1}) \)	None		✓			105.2.d.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}+q^{4}+(-2 i+1)q^{5}+\cdots\)
105.2.d.b	$105$	$2$	105.d	5.b	$2$	$6$	$6$	$0.838$	6.0.350464.1	None		✓	✓		105.2.d.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{3}+\beta _{5})q^{4}+\cdots\)

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

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