Space of modular forms of level 1665, weight 2, and Character 1665.g

• Label: 1665.2.g
• Level: $1665$
• Weight: $2$
• Character orbit: 1665.g
• Rep. character: $\chi_{1665}(739,\cdot)$
• Character field: $\Q$
• Dimension: $92$
• Newform subspaces: $5$
• Sturm bound: $456$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 1665 = 3^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1665.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 185 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(456\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1665, [\chi])\).

	Total	New	Old
Modular forms	236	96	140
Cusp forms	220	92	128
Eisenstein series	16	4	12

Trace form

92 * q + 84 * q^4 - 8 * q^10 - 8 * q^11 + 68 * q^16 - 24 * q^25 + 16 * q^26 + 16 * q^34 - 28 * q^40 - 8 * q^41 - 16 * q^44 - 104 * q^46 - 92 * q^49 + 132 * q^64 + 36 * q^65 + 52 * q^70 + 20 * q^74 - 4 * q^85 - 8 * q^86 - 44 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(1665, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1665.2.g.a	$1665$	$2$	1665.g	185.d	$2$	$4$	$4$	$13.295$	\(\Q(\sqrt{-5}, \sqrt{37})\)	\(\Q(\sqrt{-555}) \)		✓			1665.2.g.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{4}-\beta _{1}q^{5}+\beta _{3}q^{13}+4q^{16}+\cdots\)
1665.2.g.b	$1665$	$2$	1665.g	185.d	$2$	$16$	$16$	$13.295$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					185.2.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{2}+(1-\beta _{2})q^{4}-\beta _{14}q^{5}+\beta _{3}q^{7}+\cdots\)
1665.2.g.c	$1665$	$2$	1665.g	185.d	$2$	$16$	$16$	$13.295$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			1665.2.g.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{8}q^{2}+(1+\beta _{5})q^{4}+(-\beta _{6}+\beta _{7}+\cdots)q^{5}+\cdots\)
1665.2.g.d	$1665$	$2$	1665.g	185.d	$2$	$16$	$16$	$13.295$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	\(\Q(\sqrt{-111}) \)		✓			1665.2.g.d	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{12}q^{2}+(2+\beta _{15})q^{4}+\beta _{6}q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots\)
1665.2.g.e	$1665$	$2$	1665.g	185.d	$2$	$40$	$40$	$13.295$		None			✓		555.2.g.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1665, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1665, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 2}\)