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

• Label: 105.2.i
• Level: $105$
• Weight: $2$
• Character orbit: 105.i
• Rep. character: $\chi_{105}(16,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $12$
• Newform subspaces: $4$
• Sturm bound: $32$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(32\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	40	12	28
Cusp forms	24	12	12
Eisenstein series	16	0	16

Trace form

12 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 + 2 * q^7 - 24 * q^8 - 6 * q^9 + 4 * q^10 + 4 * q^11 + 4 * q^12 - 4 * q^13 - 4 * q^14 - 8 * q^16 - 8 * q^17 + 4 * q^18 - 6 * q^19 + 16 * q^20 - 12 * q^21 + 24 * q^22 + 8 * q^23 - 12 * q^24 - 6 * q^25 - 8 * q^26 - 4 * q^27 + 24 * q^28 - 8 * q^29 - 6 * q^31 + 8 * q^32 + 8 * q^33 - 16 * q^34 + 8 * q^35 + 8 * q^36 + 10 * q^37 + 32 * q^38 + 6 * q^39 + 12 * q^40 + 8 * q^41 - 4 * q^42 - 44 * q^43 + 4 * q^44 - 8 * q^46 - 8 * q^47 - 16 * q^48 - 14 * q^49 - 8 * q^50 + 4 * q^51 - 16 * q^53 - 24 * q^55 - 36 * q^56 + 12 * q^57 - 20 * q^58 + 4 * q^59 - 4 * q^61 + 24 * q^62 + 2 * q^63 + 64 * q^64 - 12 * q^65 - 12 * q^66 + 14 * q^67 + 12 * q^68 + 24 * q^69 - 4 * q^70 + 32 * q^71 + 12 * q^72 - 10 * q^73 - 4 * q^74 + 2 * q^75 + 40 * q^76 + 44 * q^77 + 8 * q^78 + 6 * q^79 - 16 * q^80 - 6 * q^81 - 28 * q^82 + 8 * q^83 + 48 * q^84 + 8 * q^85 + 20 * q^86 + 24 * q^87 + 8 * q^88 + 16 * q^89 - 8 * q^90 + 10 * q^91 - 88 * q^92 - 6 * q^93 - 24 * q^94 - 24 * q^96 - 32 * q^97 - 8 * q^99

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.i.a	$105$	$2$	105.i	7.c	$3$	$2$	$1$	$0.838$	\(\Q(\sqrt{-3}) \)	None		✓			105.2.i.a	$2$	$0$	\(0\)	\(-1\)	\(1\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+\zeta_{6}q^{5}+\cdots\)
105.2.i.b	$105$	$2$	105.i	7.c	$3$	$2$	$1$	$0.838$	\(\Q(\sqrt{-3}) \)	None		✓			105.2.i.b	$2$	$0$	\(2\)	\(-1\)	\(-1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
105.2.i.c	$105$	$2$	105.i	7.c	$3$	$4$	$2$	$0.838$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			105.2.i.c	$2$	$0$	\(0\)	\(2\)	\(2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(1+\beta _{2})q^{5}-\beta _{3}q^{6}+\cdots\)
105.2.i.d	$105$	$2$	105.i	7.c	$3$	$4$	$2$	$0.838$	\(\Q(\zeta_{12})\)	None		✓			105.2.i.d	$2$	$0$	\(2\)	\(2\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(105, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)