Space of modular forms of level 1785, weight 2, and Character 1785.g

• Label: 1785.2.g
• Level: $1785$
• Weight: $2$
• Character orbit: 1785.g
• Rep. character: $\chi_{1785}(1429,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $7$
• Sturm bound: $576$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 1785 = 3 \cdot 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1785.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(576\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1785, [\chi])\).

	Total	New	Old
Modular forms	296	96	200
Cusp forms	280	96	184
Eisenstein series	16	0	16

Trace form

96 * q - 96 * q^4 - 96 * q^9 + 16 * q^10 - 4 * q^15 + 64 * q^16 + 8 * q^19 + 40 * q^20 - 12 * q^25 - 80 * q^26 + 16 * q^29 + 16 * q^30 - 8 * q^35 + 96 * q^36 + 32 * q^39 + 24 * q^40 - 48 * q^44 + 16 * q^46 - 96 * q^49 + 72 * q^50 - 16 * q^51 - 12 * q^55 + 48 * q^56 + 32 * q^59 - 8 * q^60 + 16 * q^61 - 32 * q^64 - 32 * q^65 - 32 * q^66 + 8 * q^69 - 24 * q^70 - 48 * q^71 - 112 * q^74 - 32 * q^75 - 48 * q^76 + 80 * q^79 - 80 * q^80 + 96 * q^81 - 4 * q^85 + 128 * q^86 - 32 * q^89 - 16 * q^90 - 32 * q^91 - 48 * q^94 - 24 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(1785, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1785.2.g.a	$1785$	$2$	1785.g	5.b	$2$	$2$	$2$	$14.253$	\(\Q(\sqrt{-1}) \)	None		✓			1785.2.g.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}+i q^{3}-2 q^{4}+(-2 i+1)q^{5}+\cdots\)
1785.2.g.b	$1785$	$2$	1785.g	5.b	$2$	$4$	$4$	$14.253$	\(\Q(\zeta_{12})\)	None		✓			1785.2.g.b	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{2} q^{2}+\beta_1 q^{3}-q^{4}+(\beta_1+2)q^{5}+\cdots\)
1785.2.g.c	$1785$	$2$	1785.g	5.b	$2$	$8$	$8$	$14.253$	8.0.386672896.3	None		✓			1785.2.g.c	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{2}-\beta _{6})q^{2}+\beta _{2}q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
1785.2.g.d	$1785$	$2$	1785.g	5.b	$2$	$12$	$12$	$14.253$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			1785.2.g.d	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{10}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1785.2.g.e	$1785$	$2$	1785.g	5.b	$2$	$14$	$14$	$14.253$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓			1785.2.g.e	$2$	$0$	\(0\)	\(0\)	\(-10\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(\beta _{7}+\beta _{8})q^{4}+(\beta _{4}+\cdots)q^{5}+\cdots\)
1785.2.g.f	$1785$	$2$	1785.g	5.b	$2$	$28$	$28$	$14.253$		None		✓			1785.2.g.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1785.2.g.g	$1785$	$2$	1785.g	5.b	$2$	$28$	$28$	$14.253$		None		✓			1785.2.g.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1785, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1785, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(595, [\chi])\)\(^{\oplus 2}\)